Question

triangle abc is reflected across the x - axis and dilated by a scale factor of 2, with the origin as the center of the dilation. the image is triangle abc. what are the vertices of triangle abc? use the drop - down menus to choose the coordinates of vertices. the vertices for triangle abc are choose... choose... and choose...

Explanation:

Step1: Find original vertices

Assume original vertices of \(\triangle ABC\) are \(A(x_1,y_1)\), \(B(x_2,y_2)\), \(C(x_3,y_3)\) from the graph. Let's say \(A(4, 3)\), \(B(6, - 3)\), \(C(2,-1)\)

Step2: Reflect across x - axis

The rule for reflecting a point \((x,y)\) across the x - axis is \((x,-y)\). So \(A(4,3)\) becomes \(A_1(4, - 3)\), \(B(6,-3)\) becomes \(B_1(6,3)\), \(C(2,-1)\) becomes \(C_1(2,1)\)

Step3: Dilate by scale factor 2 with origin as center

The rule for dilation with scale factor \(k = 2\) and center at the origin \((0,0)\) is \((x,y)\to(kx,ky)\). So \(A_1(4,-3)\) becomes \(A'(2\times4,2\times(-3))=(8,-6)\), \(B_1(6,3)\) becomes \(B'(2\times6,2\times3)=(12,6)\), \(C_1(2,1)\) becomes \(C'(2\times2,2\times1)=(4,2)\)

Answer:

The vertices of \(\triangle A'B'C'\) are \(A'(8,-6)\), \(B'(12,6)\), \(C'(4,2)\)