Question

Right triangle XYZ, has vertex angles at the coordinates, X(0, 0), Y(-3, 0) and Z(-3, 4) . Its image, triangle X'Y'Z' has vertex angles at the coordinates, X'(3, -5), Y'(0, -5), and Z'(0, -1). Describe the horizontal and vertical translations that map triangle XYZ onto its image, triangle X'Y'Z'.

Answer 1

We want the translation which maps X to X', etc.

If there is one, these will all be equal:

X' - X = (3, -5) - (0,0) = (3, -5)

Y' - Y = (0, -5) - (-3, 0) = (3, -5)

Z' - Z = (0, -1) - (-3, 4) = (3, -5)

They're all equal, and they're all our translation:

X' = X + (3, -5)

That's three units to the right, five down, last choice.

Answer 2

Right 3 ; down 5.

Explanation:

Given a right triangle XYZ has vertex angles at the coordinates X(0,0),Y (-3,0)and Z(-3,4)

The vertex angles at the coordinates X'(3,-5) ,Y'(0,-5) and Z'(0,-1) of the image triangle X'Y'Z' of given triangle XYZ.

X(0,0) change into X'(3,-5)

We can write

x'-x=3-0=3

x'=x+3

y'-y=-5-0=-5

y'=y-5

Similarly , in the same way Y(-3,0) change into (0,-5) and Z(-3,4) change into Z'(0,-1).

Hence, the horizontal translation x'=x+3 .It means shift 3 unit on the right side of x axis.

Vertical translation y'=y-5.It means shift 5 unit downward on the negative y-axis.

Option D. Right 3; down 5 is correct option.