Question

Which graph shows a dilation? On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 0.5, 0), (negative 1, 2), (1, 2), (1.5, 0).

Answer 1

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0).

Explanation:

Larger quadrilateral

Length of the top and bottom segments are 6 units.

Length of the left and right sides:

d = √[(-5 - (-2))² + (3 - 0)²] = √[3² + 3²] = √(2*3²) = 3√2 units

From point (-5, 3) to point (-2, 0) the slope is:

m = (3 - 0)/(-5 - (-2)) = -1

Smaller quadrilateral

Length of the top and bottom segments are 2 units.

Length of the left and right sides:

d = √[(-2 - (-1))² + (1 - 0)²] = √[1² + 1²] = √2 units

From point (-2, 1) to point (-1, 0) the slope is:

m = (1 - 0)/(-2 - (-1)) = -1

If you dilate the smaller quadrilateral by a factor of 3, you get the larger quadrilateral (they have the same slope, and 3 times length of the smaller quadrilateral is equal to the length of the larger quadrilateral).

Answer 2

Answer: C

Explanation: