Question

△abc is shown on the coordinate grid. △abc is transformed to form △abc with the following coordinates: a(-8,2) b(-4,8) c(0,-2) which transformation could transform △abc to △abc? dilation with a scale factor of 1/2 dilation with a scale factor of 2 translation 4 units up and 2 units to the right translation 4 units down and 2 units to the left part b △abc is translated 4 units up and 3 units to the right and is then reflected

Explanation:

Step1: Identify coordinates of △ABC

From the grid, assume \(A(-4,1)\), \(B(-2,4)\), \(C(0, - 1)\)

Step2: Check dilation with scale - factor of \(\frac{1}{2}\)

If we dilate \((x,y)\) with a scale - factor of \(\frac{1}{2}\), the new coordinates \((x',y')=(\frac{1}{2}x,\frac{1}{2}y)\). This will not give the coordinates of \(\triangle A'B'C'\)

Step3: Check dilation with scale - factor of 2

If we dilate \((x,y)\) with a scale - factor of 2, the new coordinates \((x',y')=(2x,2y)\). For \(A(-4,1)\), \(2\times(-4)= - 8\), \(2\times1 = 2\); for \(B(-2,4)\), \(2\times(-2)=-4\), \(2\times4 = 8\); for \(C(0,-1)\), \(2\times0 = 0\), \(2\times(-1)=-2\). This gives the coordinates of \(\triangle A'B'C'\)

Step4: Check translation 4 units up and 2 units to the right

The translation rule is \((x,y)\to(x + 2,y + 4)\). This will not give the coordinates of \(\triangle A'B'C'\)

Step5: Check translation 4 units down and 2 units to the left

The translation rule is \((x,y)\to(x-2,y - 4)\). This will not give the coordinates of \(\triangle A'B'C'\)

Answer:

Dilation with a scale factor of 2