Question

Triangle J′K′L′ shown on the grid below is a dilation of triangle JKL using the origin as the center of dilation: Two triangles on a grid. First triangle has vertices J 4 and 6, K 2 and 4, and L 6 and 3. Image triangle has vertices J prime 8 and 12, K prime 4 and 8, L prime 12 and 6. Which scale factor was used to create triangle J′K′L′?

A. 4
B. 2
C. one quarter
D. one half

Answer 1

B) 2

Explanation:

To find the scale factor used to create triangle J′K′L′ from triangle JKL, you can compare the corresponding side lengths of the two triangles. The scale factor is the ratio of the corresponding side lengths.

Let's calculate the side lengths for both triangles:

For triangle JKL:

Side JK has length = √((2 - 4)^2 + (4 - 6)^2) = √(4 + 4) = √8.

Side KL has length = √((6 - 2)^2 + (3 - 4)^2) = √(16 + 1) = √17.

Side LJ has length = √((4 - 6)^2 + (6 - 3)^2) = √(4 + 9) = √13.

For triangle J′K′L′:

Side J′K′ has length = √((4 - 8)^2 + (8 - 12)^2) = √(16 + 16) = √32.

Side K′L′ has length = √((8 - 12)^2 + (12 - 6)^2) = √(16 + 36) = √52.

Side L′J′ has length = √((12 - 8)^2 + (6 - 12)^2) = √(16 + 36) = √52.

Now, let's find the scale factor by comparing the corresponding side lengths:

Scale factor = (J′K′ length) / (JK length) = √32 / √8

Scale factor = (√(32/8)) = √4 = 2.

So, the scale factor used to create triangle J′K′L′ from triangle JKL is 2.