Question

draw the image of △abc under a dilation whose center is p and scale factor is 2.

Explanation:

Step1: Connect center P to vertices

Draw lines from point P to points A, B, and C.

Step2: Extend the lines

Extend the lines PA, PB, and PC such that the new distances from P to the new - vertices are twice the original distances. For example, if the distance from P to A is \(d_{PA}\), the distance from P to the new point \(A'\) (the image of A) is \(2d_{PA}\).

Step3: Mark the new vertices

Mark the new points \(A'\), \(B'\), and \(C'\) at the end - points of the extended lines.

Step4: Draw the new triangle

Connect points \(A'\), \(B'\), and \(C'\) to form the dilated triangle \(\triangle A'B'C'\).

Since this is a drawing problem, a visual answer cannot be directly provided in text. The steps above describe how to draw the image of \(\triangle ABC\) under a dilation with center \(P\) and scale factor 2. In a grid - based system, you can count the grid units between the center \(P\) and the vertices of \(\triangle ABC\) and then double those distances to find the new vertices of the dilated triangle.

Answer:

Step1: Connect center P to vertices

Draw lines from point P to points A, B, and C.

Step2: Extend the lines

Extend the lines PA, PB, and PC such that the new distances from P to the new - vertices are twice the original distances. For example, if the distance from P to A is \(d_{PA}\), the distance from P to the new point \(A'\) (the image of A) is \(2d_{PA}\).

Step3: Mark the new vertices

Mark the new points \(A'\), \(B'\), and \(C'\) at the end - points of the extended lines.

Step4: Draw the new triangle

Connect points \(A'\), \(B'\), and \(C'\) to form the dilated triangle \(\triangle A'B'C'\).

Since this is a drawing problem, a visual answer cannot be directly provided in text. The steps above describe how to draw the image of \(\triangle ABC\) under a dilation with center \(P\) and scale factor 2. In a grid - based system, you can count the grid units between the center \(P\) and the vertices of \(\triangle ABC\) and then double those distances to find the new vertices of the dilated triangle.