Question

triangle abc has vertices a(1,4), b(-2,4), and c(-1,-1). a dilation with a scale factor of 0.25 and center at the origin is applied to the triangle. what are the coordinates of b in the dilated image? enter your answer by filling in the boxes. b has a coordinate pair of (□,□)

Explanation:

Step1: Recall dilation formula

For a dilation with scale - factor \(k\) centered at the origin, if a point \(P(x,y)\) is dilated, the new point \(P'(x',y')\) has coordinates \(x' = kx\) and \(y'=ky\). Here \(k = 0.25\), and the coordinates of point \(B\) are \((-2,4)\).

Step2: Calculate \(x\) - coordinate of \(B'\)

\(x'=0.25\times(-2)=- 0.5\)

Step3: Calculate \(y\) - coordinate of \(B'\)

\(y'=0.25\times4 = 1\)

Answer:

\((-0.5,1)\)