Question

find the new points for the translation of triangle jkl with vertices j(-2, 3), k(2, 4), and l(6, -1): (x, y) → (x - 2, y - 6)

Explanation:

Step1: Translate point J(-2, 3)

To translate \( J(-2, 3) \) using \( (x, y) \to (x - 2, y - 6) \), substitute \( x = -2 \) and \( y = 3 \) into the translation rule.
\( x - 2 = -2 - 2 = -4 \)
\( y - 6 = 3 - 6 = -3 \)
So the new point for \( J \) is \( (-4, -3) \).

Step2: Translate point K(2, 4)

For \( K(2, 4) \), substitute \( x = 2 \) and \( y = 4 \) into the translation rule.
\( x - 2 = 2 - 2 = 0 \)
\( y - 6 = 4 - 6 = -2 \)
So the new point for \( K \) is \( (0, -2) \).

Step3: Translate point L(6, -1)

For \( L(6, -1) \), substitute \( x = 6 \) and \( y = -1 \) into the translation rule.
\( x - 2 = 6 - 2 = 4 \)
\( y - 6 = -1 - 6 = -7 \)
So the new point for \( L \) is \( (4, -7) \).

Answer:

The new points after translation are \( J'(-4, -3) \), \( K'(0, -2) \), and \( L'(4, -7) \).