Question

1. triangle abc is shown on the coordinate plane below. the triangle is dilated from the origin by scale factor r = 4. identify the coordinates of the dilated triangle abc.

Explanation:

1. First, identify the coordinates of the original - triangle \(ABC\):

• By observing the graph, assume the coordinates of point \(A\) are \((- 10,6)\), the coordinates of point \(B\) are \((-10,2)\), and the coordinates of point \(C\) are \((-4,4)\).
• The rule for dilation from the origin by a scale - factor \(r\) is \((x,y)\to(rx,ry)\). Here, \(r = 4\).

Step1: Find the coordinates of \(A'\)

• For point \(A(-10,6)\), using the dilation formula \((x,y)\to(rx,ry)\) with \(r = 4\), we have \(x=-10\) and \(y = 6\). Then \(x'=4\times(-10)=-40\) and \(y'=4\times6 = 24\). So, the coordinates of \(A'\) are \((-40,24)\).

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

• For point \(B(-10,2)\), with \(x=-10\) and \(y = 2\) and \(r = 4\), we get \(x'=4\times(-10)=-40\) and \(y'=4\times2=8\). So, the coordinates of \(B'\) are \((-40,8)\).

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

• For point \(C(-4,4)\), with \(x=-4\) and \(y = 4\) and \(r = 4\), we have \(x'=4\times(-4)=-16\) and \(y'=4\times4 = 16\). So, the coordinates of \(C'\) are \((-16,16)\).

Answer:

The coordinates of \(A'\) are \((-40,24)\), the coordinates of \(B'\) are \((-40,8)\), and the coordinates of \(C'\) are \((-16,16)\).