Question

triangle def has coordinates
d(-3, -2), e(-1, -2), f(-2, -4).
the triangle is translated so its image has coordinates
d(1, -4), e(3, -4), f(2, -6).
which statement shows the rule for the translation?
○ (x, y) → (x - 4, y - 2)
○ (x, y) → (x - 4, y + 2)
○ (x, y) → (x + 4, y + 2)
○ (x, y) → (x + 4, y - 2)

Explanation:

Step1: Analyze x - coordinate change (D)

Original \( x \): \(-3\), New \( x \): \(1\). Change: \(1 - (-3)=4\), so \(x\) increases by 4 (\(x + 4\)).

Step2: Analyze y - coordinate change (D)

Original \( y \): \(-2\), New \( y \): \(-4\). Change: \(-4 - (-2)=-2\), so \(y\) decreases by 2 (\(y - 2\)).

Step3: Verify with E

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

Step4: Verify with F

Original \( F(-2,-4) \): \(x=-2 + 4 = 2\), \(y=-4 - 2=-6\) (matches \(F'(2,-6)\)).

Answer:

\((x,y)\to(x + 4,y - 2)\)