Question

∆MUG has coordinates M(10, -3), U(5, 2), and G(4, 6). A translation maps point M to M'(4, 1). What are the coordinates of U' and G' for this translation?

Answer 1

In order to find the coordinates of U' and G', let's first find the transformation from M to M'

Calculating the difference of x and y coordinates, we have:

`\begin{gathered} M_x-M^(\prime)_x=4-10=-6 \\ M_y-M^(\prime)_y=1-(-3)=4 \end{gathered}`

So the transformation is a translation of 6 units to the left (-6) and 4 units up (+4).

Then, applying this transformation to the points U and G, we have:

`\begin{gathered} U(5,2)\to U^(\prime)(5-6,2+4)=U^(\prime)(-1,6)_{} \\ G(4,6)\to G^(\prime)(4-6,6+4)=G^(\prime)(-2,10) \end{gathered}`