Question

A dilation maps triangle HIJ onto triangle H'I'J. If HI= 7 cm, IJ= 7 cm, I’J’= 5.25 cm, and H’J= 9 cm, the find HJ.

a. 4.08 cm
b. 6.75 cm
c. 9 cm
d. 12 cm

Answer 1

To find HJ, we calculate the scale factor of the dilation (0.75), then divide the length of H'J by this scale factor to find that HJ is 12 cm.

Step-by-step explanation:

To find the length of side HJ in the original triangle HIJ after a dilation mapping to triangle H'I'J', we first need to determine the scale factor of the dilation. Given that side IJ equals 7 cm and its image I'J' equals 5.25 cm, we can find the scale factor by dividing the length of I'J' by IJ:

Scale factor = I'J' / IJ = 5.25 cm / 7 cm = 0.75

Now that we have the scale factor, we can use it to find the length of side HJ. We are given that H'J = 9 cm, which is the image of HJ after dilation. Since the dilation reduces the lengths by a factor of 0.75, we can find HJ by dividing H'J by the scale factor:

HJ = H'J / Scale factor = 9 cm / 0.75 = 12 cm

Therefore, the correct answer is d. 12 cm.