Question

Triangle PQR is dilated using the origin as the center to form the image triangle P'Q'R. Determine the scale factor used to make this transformation

Answer 1

Scale factor = 3

Step-by-step explanation:

Where we dilate a figure by a scale factor of k, the coordinates of all the vertex are transformed using the rule:

(x, y) = (k*x, k*y)

So, in order to identify the scale factor, we need to identify the coordinates of points P, Q, and R and points P', Q', and R'. Then:

P(1, 3) ------> P'(3, 9)

Q(3, 1) ------> Q'(9, 3)

R(1, 1) -------> R'(3, 3)

Therefore, the scale factor is 3, because:

P(1, 3) ------>(3*1, 3*3) = P'(3, 9)

Q(3, 1) ------>(3*3, 3*1) = Q'(9, 3)

R(1, 1) ------->(3*1, 3*1) = R'(3, 3)