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Reading and writing coordinates, translating a point, and finding a missing corner.
Question 1 of 12
Three corners of a rectangle are at (-4, 3), (2, 3) and (-4, 9). Where is the fourth corner?
Two of the given corners share the same y value (3), so they form the bottom edge, running from x = -4 to x = 2. Two share the same x value (-4), forming the left edge from y = 3 to y = 9. The fourth corner is diagonally opposite (-4, 3): it takes its x from one neighbour and its y from the other, giving (2, 9). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
The answer is A. Two of the given corners share the same y value (3), so they form the bottom edge, running from x = -4 to x = 2. Two share the same x value (-4), forming the left edge from y = 3 to y = 9. The fourth corner is diagonally opposite (-4, 3): it takes its x from one neighbour and its y from the other, giving (2, 9). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
Three corners of a rectangle are at (2, -4), (8, -4) and (2, 0). Where is the fourth corner?
Two of the given corners share the same y value (-4), so they form the bottom edge, running from x = 2 to x = 8. Two share the same x value (2), forming the left edge from y = -4 to y = 0. The fourth corner is diagonally opposite (2, -4): it takes its x from one neighbour and its y from the other, giving (8, 0). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
The answer is B. Two of the given corners share the same y value (-4), so they form the bottom edge, running from x = 2 to x = 8. Two share the same x value (2), forming the left edge from y = -4 to y = 0. The fourth corner is diagonally opposite (2, -4): it takes its x from one neighbour and its y from the other, giving (8, 0). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
The point (-4, 2) is translated 2 down. What are its new coordinates?
Coordinates are written across first, then up: (x, y). Moving 2 down changes the y from 2 to 0, giving (-4, 0). Left and down make the number smaller even when that means going further below zero. Right and up add; left and down subtract. Negatives follow the same rule.
The answer is B. Coordinates are written across first, then up: (x, y). Moving 2 down changes the y from 2 to 0, giving (-4, 0). Left and down make the number smaller even when that means going further below zero. Right and up add; left and down subtract. Negatives follow the same rule.
The point (-5, 1) is translated 5 right and 3 up. What are its new coordinates?
Coordinates are written across first, then up: (x, y). Moving 5 right and 3 up changes the x from -5 to 0 and the y from 1 to 4, giving (0, 4). Left and down make the number smaller even when that means going further below zero. Right and up add; left and down subtract. Negatives follow the same rule.
The answer is A. Coordinates are written across first, then up: (x, y). Moving 5 right and 3 up changes the x from -5 to 0 and the y from 1 to 4, giving (0, 4). Left and down make the number smaller even when that means going further below zero. Right and up add; left and down subtract. Negatives follow the same rule.
The point (4, -2) is translated 4 right and 2 down. What are its new coordinates?
Coordinates are written across first, then up: (x, y). Moving 4 right and 2 down changes the x from 4 to 8 and the y from -2 to -4, giving (8, -4). Left and down make the number smaller even when that means going further below zero. Write the brackets and the comma. A pair of coordinates without them is easy to misread.
The answer is A. Coordinates are written across first, then up: (x, y). Moving 4 right and 2 down changes the x from 4 to 8 and the y from -2 to -4, giving (8, -4). Left and down make the number smaller even when that means going further below zero. Write the brackets and the comma. A pair of coordinates without them is easy to misread.
Three corners of a rectangle are at (2, -2), (9, -2) and (2, 3). Where is the fourth corner?
Two of the given corners share the same y value (-2), so they form the bottom edge, running from x = 2 to x = 9. Two share the same x value (2), forming the left edge from y = -2 to y = 3. The fourth corner is diagonally opposite (2, -2): it takes its x from one neighbour and its y from the other, giving (9, 3). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
The answer is D. Two of the given corners share the same y value (-2), so they form the bottom edge, running from x = 2 to x = 9. Two share the same x value (2), forming the left edge from y = -2 to y = 3. The fourth corner is diagonally opposite (2, -2): it takes its x from one neighbour and its y from the other, giving (9, 3). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
Three corners of a rectangle are at (-1, 3), (1, 3) and (-1, 9). Where is the fourth corner?
Two of the given corners share the same y value (3), so they form the bottom edge, running from x = -1 to x = 1. Two share the same x value (-1), forming the left edge from y = 3 to y = 9. The fourth corner is diagonally opposite (-1, 3): it takes its x from one neighbour and its y from the other, giving (1, 9). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
The answer is A. Two of the given corners share the same y value (3), so they form the bottom edge, running from x = -1 to x = 1. Two share the same x value (-1), forming the left edge from y = 3 to y = 9. The fourth corner is diagonally opposite (-1, 3): it takes its x from one neighbour and its y from the other, giving (1, 9). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
Three corners of a rectangle are at (-4, 0), (-2, 0) and (-4, 7). Where is the fourth corner?
Two of the given corners share the same y value (0), so they form the bottom edge, running from x = -4 to x = -2. Two share the same x value (-4), forming the left edge from y = 0 to y = 7. The fourth corner is diagonally opposite (-4, 0): it takes its x from one neighbour and its y from the other, giving (-2, 7). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
The answer is A. Two of the given corners share the same y value (0), so they form the bottom edge, running from x = -4 to x = -2. Two share the same x value (-4), forming the left edge from y = 0 to y = 7. The fourth corner is diagonally opposite (-4, 0): it takes its x from one neighbour and its y from the other, giving (-2, 7). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
The point (1, 5) is translated 3 right and 3 down. What are its new coordinates?
Coordinates are written across first, then up: (x, y). Moving 3 right and 3 down changes the x from 1 to 4 and the y from 5 to 2, giving (4, 2). Left and down make the number smaller even when that means going further below zero. Along the corridor, then up the stairs. It is the oldest way of remembering which number comes first, and it works.
The answer is C. Coordinates are written across first, then up: (x, y). Moving 3 right and 3 down changes the x from 1 to 4 and the y from 5 to 2, giving (4, 2). Left and down make the number smaller even when that means going further below zero. Along the corridor, then up the stairs. It is the oldest way of remembering which number comes first, and it works.
Three corners of a rectangle are at (0, 1), (3, 1) and (0, 6). Where is the fourth corner?
Two of the given corners share the same y value (1), so they form the bottom edge, running from x = 0 to x = 3. Two share the same x value (0), forming the left edge from y = 1 to y = 6. The fourth corner is diagonally opposite (0, 1): it takes its x from one neighbour and its y from the other, giving (3, 6). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
The answer is D. Two of the given corners share the same y value (1), so they form the bottom edge, running from x = 0 to x = 3. Two share the same x value (0), forming the left edge from y = 1 to y = 6. The fourth corner is diagonally opposite (0, 1): it takes its x from one neighbour and its y from the other, giving (3, 6). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
Three corners of a rectangle are at (1, 1), (6, 1) and (1, 7). Where is the fourth corner?
Two of the given corners share the same y value (1), so they form the bottom edge, running from x = 1 to x = 6. Two share the same x value (1), forming the left edge from y = 1 to y = 7. The fourth corner is diagonally opposite (1, 1): it takes its x from one neighbour and its y from the other, giving (6, 7). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
The answer is C. Two of the given corners share the same y value (1), so they form the bottom edge, running from x = 1 to x = 6. Two share the same x value (1), forming the left edge from y = 1 to y = 7. The fourth corner is diagonally opposite (1, 1): it takes its x from one neighbour and its y from the other, giving (6, 7). Sketching the three points on squared paper makes the missing one obvious. In a rectangle the opposite corner shares one coordinate with each of its neighbours.
Three corners of a rectangle are at (4, 1), (7, 1) and (4, 5). Where is the fourth corner?
Two of the given corners share the same y value (1), so they form the bottom edge, running from x = 4 to x = 7. Two share the same x value (4), forming the left edge from y = 1 to y = 5. The fourth corner is diagonally opposite (4, 1): it takes its x from one neighbour and its y from the other, giving (7, 5). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
The answer is A. Two of the given corners share the same y value (1), so they form the bottom edge, running from x = 4 to x = 7. Two share the same x value (4), forming the left edge from y = 1 to y = 5. The fourth corner is diagonally opposite (4, 1): it takes its x from one neighbour and its y from the other, giving (7, 5). Sketching the three points on squared paper makes the missing one obvious. Look for the pairs that share an x or a y. They tell you which edges you already have.
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