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:

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