Question

Points M (3,4) and T(-2, 3) form MT. The translation (x, y) -> (x + h,y + k) is applied to MT', such that M' (7, 1) and I' (2, 0).

Complete the algebraic description of the translation.
(x,y) -> (x+ h,y + k)

h=
k=

Answer 1

(x, y) → (x + 4, y - 3)

h = 4

k = -3

Explanation:

Given points:

• M = (3, 4)
• M' = (7, 1)
• T = (-2, 3)
• T' = (2, 0)

Given translation:

(x, y) → (x+h, y+k)

To find the value of h, subtract the x-values of points M and T from the x-values of points M' and T':

`\begin{aligned}\implies h&=x_(M')-x_M\\&=7-3\\&=4\end{aligned}`

`\begin{aligned}\implies h&=x_(T')-x_T\\&=2-(-2)\\&=4\end{aligned}`

To find the value of k, subtract the y-values of points M and T from the y-values of points M' and T':

`\begin{aligned}\implies k&=y_(M')-y_M\\&=1-4\\&=-3\end{aligned}`

`\begin{aligned}\implies k&=y_(T')-y_Y\\&=0-3\\&=-3\end{aligned}`

Therefore the algebraic description of the translation is:

(x, y) → (x + 4, y - 3)