Question

x (-2,3) y (-2,-1) z (3,-1) lina dilates △xyz with scale factor 3 with the center choose x (-6,9) z (1,-3) y (-4,-2) z (9,-3) x (9,-6) y (-6,-3) choose choose

Explanation:

Step1: Recall the dilation formula

If a point \(P(x,y)\) is dilated with a scale factor \(k\) and center at the origin \((0,0)\), the new point \(P'(x',y')\) is given by \(x'=k\times x\) and \(y' = k\times y\). Here \(k = 3\).

Step2: Find the coordinates of \(X'\)

For \(X(-2,3)\), using the formula \(x'=3\times(-2)=-6\) and \(y'=3\times3 = 9\). So \(X'(-6,9)\).

Step3: Find the coordinates of \(Y'\)

For \(Y(-2,-1)\), using the formula \(x'=3\times(-2)=-6\) and \(y'=3\times(-1)=-3\). So \(Y'(-6,-3)\).

Step4: Find the coordinates of \(Z'\)

For \(Z(3,-1)\), using the formula \(x'=3\times3 = 9\) and \(y'=3\times(-1)=-3\). So \(Z'(9,-3)\).

Answer:

X' (-6, 9), Y' (-6, -3), Z' (9, -3)