given △abc, use a dilation with the center at the origin to make a similar triangle with side lengths three…

given △abc, use a dilation with the center at the origin to make a similar triangle with side lengths three times as large. what are the coordinates of c of the image? (-6, 3) (-3, 6) (3, -6) (6, -3)

given △abc, use a dilation with the center at the origin to make a similar triangle with side lengths three times as large. what are the coordinates of c of the image? (-6, 3) (-3, 6) (3, -6) (6, -3)

Answer

Explanation:

Step1: Identify coordinates of C

From the graph, the coordinates of point C are (2, -1).

Step2: Apply dilation rule

For a dilation with center at the origin and scale - factor (k = 3), the rule for dilation is ((x,y)\to(kx,ky)). Here (x = 2) and (y=-1), so (C'=(3\times2,3\times(-1))).

Step3: Calculate new coordinates

(3\times2 = 6) and (3\times(-1)=-3). So the coordinates of (C') are ((6, - 3)).

Answer:

(6, -3)