Question

7. Triangle XYZ is the preimage of triangle XYZ Find: a. Length of XZ = (show your work) b. Length of X'Z'= (Show your work) C. Scale factor from XZ to XZ = (Show your work X'Z'=6/4. XZ=3/2

Answer 1

a) The length of XZ can be calculated by the distance formula.

The coordinates of X are (-2,2) and the coordinates of Z are (0,-1).

The distance is:

`D=\sqrt[]{(2-(-1)^2+(-2-0)^2}=\sqrt[]{3^2+(-2)^2=\sqrt[]{9+4=\sqrt[]{13}\approx}}3.6`

Length of XZ = square root of 13 (approximately 3.6)

b) The coordinates of X' are (-4,4) and the coordinates of Z' are (0,-2).

The distance between X' and Z' is:

`D=\sqrt[]{(4-(-2)^2+(-4-0)^2}=\sqrt[]{6^2+(-4)^2=\sqrt[]{36+16=\sqrt[]{52}=\sqrt[]{4\cdot13}}}=2\sqrt[]{13\approx}7.2`

Length of X'Z' = two times the square root of 13 (approximately 7.2)

c) The scale factor can be calculated as the ratio between two segments.

In this case, as we have calculated X'Z' and XZ, we are using them:

`k=\frac{X\text{'Z'}}{XZ}=\frac{2\sqrt[]{13}}{\sqrt[]{13}}=2`

The scale factor is k=2.

We could have calculated it with the coordinates of one point also.