Question

14 fill in the blank 3 points given that △aeb was changed to create △ced, find the scale factor that was used and then find the coordinates for c. dado que △aeb fue cambiado para crear △ced, encontrar el factor de escala que fue utilizado y luego encontrar las coordenadas para c. a(0, 2) e(0, 0) b(3, 0) d(9, 0) scale factor (factor de escala) type your answer. c( type your answer. type your answer. )

Explanation:

Step1: Calculate scale - factor

The distance between \(E(0,0)\) and \(B(3,0)\) is \(EB = 3-0=3\), and the distance between \(E(0,0)\) and \(D(9,0)\) is \(ED = 9 - 0=9\). The scale - factor \(k\) is given by the ratio of the corresponding side lengths of the two similar triangles \(\triangle AEB\) and \(\triangle CED\). So, \(k=\frac{ED}{EB}=\frac{9}{3}=3\).

Step2: Find coordinates of C

The \(x\) - coordinate of \(A\) is \(0\) and the \(y\) - coordinate of \(A\) is \(2\). Since the center of dilation is at the origin \(E(0,0)\), to find the coordinates of \(C\) (corresponding to \(A\) in the dilated triangle), we multiply the coordinates of \(A\) by the scale - factor. The \(x\) - coordinate of \(C\) is \(0\times3 = 0\), and the \(y\) - coordinate of \(C\) is \(2\times3=6\).

Answer:

Scale factor: 3
C(0, 6)