On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) and (negative 2.5, negative 6). Quadrilateral Q prime R prime S prime T prime has points (negative 1, 2), (1, 2), (0.5, 0), and (negative 1.5, 0).
Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?

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Lanuel Lanuel · Answer 1 · 2022-07-18T20:25:47+02:00

Based on the calculations, the scale factor for this dilation is equal to 1/3.

First of all, we would use the distance formula to find the length of side QR and Q'R' as follows:

Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]

Substituting the given points into the formula, we have;

Distance QR = √[(5 - (-1))² + (0 - 0)²]

Distance QR = √[(5 + 1)² + (0)²]

Distance QR = √[6² + 0]

Distance QR = √36

Distance QR = 6 units.

For side Q'R', we have:

Distance Q'R' = √[(1 - (-1))² + (2 - 2)²]

Distance Q'R' = √[(1 + 1)² + (0)²]

Distance Q'R' = √[2² + 0]

Distance Q'R' = √4

Distance Q'R' = 2 units.

Now, the scale factor for this dilation is given by:

Scale factor = Q'R'/QR

Scale factor = 2/6

Scale factor = 1/3.

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