Question

the graph shows quadrilaterals defg and defg.
which of the following transformations maps defg onto defg?
translation left 10 units and up 12 units
translation left 6 units and up 16 units
reflection across the x-axis
reflection across the y-axis
rotation 90° clockwise around the origin
rotation 90° counterclockwise around the origin
rotation 180° around the origin

Explanation:

Step1: Identify coordinates of a point

Take point $E$: $E=(3, -3)$, $E'=(-7, 9)$

Step2: Calculate horizontal translation

$\Delta x = -7 - 3 = -10$ (left 10 units)

Step3: Calculate vertical translation

$\Delta y = 9 - (-3) = 12$ (up 12 units)

Step4: Verify with another point

Take point $G$: $G=(6, -9)$, $G'=(-4, 3)$. $\Delta x=-4-6=-10$, $\Delta y=3-(-9)=12$. Matches.

Answer:

translation left 10 units and up 12 units