Question

problem 7 here is triangle abc. drag the points to dilate each vertex of triangle abc using point p as the center of dilation and a scale factor of 2. then press the button below to draw the triangle. draw triangle

Explanation:

Step1: Recall dilation formula

If the center of dilation is \(P(x_p,y_p)\) and a vertex of the original triangle is \(A(x_a,y_a)\) and the scale - factor is \(k\), the coordinates of the dilated point \(A'(x_{a'},y_{a'})\) are given by \(x_{a'}=x_p + k(x_a - x_p)\) and \(y_{a'}=y_p + k(y_a - y_p)\). Here \(k = 2\).

Step2: Dilate vertex A

Let's assume \(P\) is the origin of the coordinate - grid for simplicity (if no coordinates are given otherwise). If \(A(x_a,y_a)\) is a vertex of \(\triangle ABC\), then \(A'=2A\). Measure the grid distances of point \(A\) from \(P\). If \(A\) is \(m\) units horizontally and \(n\) units vertically from \(P\), then \(A'\) will be \(2m\) units horizontally and \(2n\) units vertically from \(P\).

Step3: Dilate vertex B

Similarly, for vertex \(B(x_b,y_b)\), the dilated vertex \(B'\) has coordinates \(x_{b'}=2x_b\) and \(y_{b'}=2y_b\) (assuming \(P\) is at the origin). Measure the grid distances of \(B\) from \(P\) and double them to find \(B'\).

Step4: Dilate vertex C

For vertex \(C(x_c,y_c)\), the dilated vertex \(C'\) has coordinates \(x_{c'}=2x_c\) and \(y_{c'}=2y_c\) (assuming \(P\) is at the origin). Measure the grid distances of \(C\) from \(P\) and double them to find \(C'\).

Step5: Connect the dilated vertices

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

Answer:

Draw the new triangle by doubling the distances of \(A\), \(B\), and \(C\) from point \(P\) and connecting the new points \(A'\), \(B'\), and \(C'\).