Question

a triangle has coordinates f(-2, 3), g(-4, 1), and h(-2, -2). the triangle is translated and its image has coordinates f’(0, 0), g’(-2, -2), and h’(0, -5). what is the correct rule for the translation?
○ (x,y) → (x + 2, y + 3)
○ (x,y) → (x + 2, y − 3)
○ (x,y) → (x − 2, y + 3)
○ (x,y) → (x − 3, y + 2)

Explanation:

Step1: Analyze x - coordinate change (F)

Original x: \(-2\), New x: \(0\). Change: \(0 - (-2)=2\), so \(x\) increases by \(2\) (i.e., \(x + 2\)).

Step2: Analyze y - coordinate change (F)

Original y: \(3\), New y: \(0\). Change: \(0 - 3=-3\), so \(y\) decreases by \(3\) (i.e., \(y - 3\)).

Step3: Verify with G

Original G: \((-4,1)\). Apply \((x + 2,y - 3)\): \(-4 + 2=-2\), \(1-3=-2\), matches \(G'(-2,-2)\).

Step4: Verify with H

Original H: \((-2,-2)\). Apply \((x + 2,y - 3)\): \(-2 + 2 = 0\), \(-2-3=-5\), matches \(H'(0,-5)\).

Answer:

\((x,y)\to(x + 2,y - 3)\)