Question

triangle abc has vertices located at a(-3, 3), b(-2, 3) and c(1, 2). triangle abc is the result of dilating triangle abc using point o(-5, 1) as the center of dilation and a scale factor of 3. draw triangle abc and its image on the coordinate plane.

Explanation:

Step1: Recall dilation formula

The formula for dilation with center \((h,k)\) and scale - factor \(s\) is \((x,y)\to(h + s(x - h),k + s(y - k))\). Here \(h=-5,k = 1,s = 3\).

Step2: Find the image of point A

For point \(A(-3,3)\), using the dilation formula:

$$
LATEXBLOCK0
$$

Step3: Find the image of point B

For point \(B(-2,3)\), using the dilation formula:

$$
LATEXBLOCK1
$$

Step4: Find the image of point C

For point \(C(1,2)\), using the dilation formula:

$$
LATEXBLOCK2
$$

To draw:

1. Plot the points \(A(-3,3)\), \(B(-2,3)\) and \(C(1,2)\) on the coordinate - plane and connect them to form \(\triangle ABC\).
2. Plot the points \(A'(1,7)\), \(B'(4,7)\) and \(C'(13,4)\) on the coordinate - plane and connect them to form the dilated triangle \(A'B'C'\).

Answer:

The vertices of the dilated triangle are \(A'(1,7)\), \(B'(4,7)\) and \(C'(13,4)\). Plot \(\triangle ABC\) with \(A(-3,3)\), \(B(-2,3)\), \(C(1,2)\) and \(\triangle A'B'C'\) with \(A'(1,7)\), \(B'(4,7)\), \(C'(13,4)\) on the coordinate plane.