Question

polygon abcde is dilated by a scale factor of 3, with the center of dilation at the origin, to create polygon abcde. if the endpoints of bc are b(3,5) and c(5,10), what is the slope of bc? type the correct answer in the box. use numerals instead of words. round any decimal answers to the nearest tenth. m =

Explanation:

Step1: Find coordinates of \(B'\) and \(C'\)

When a point \((x,y)\) is dilated by a scale factor \(k\) with the center of dilation at the origin \((0,0)\), the new - point is \((kx,ky)\).
For point \(B(3,5)\), after dilation with \(k = 3\), \(B'=(3\times3,5\times3)=(9,15)\).
For point \(C(5,10)\), after dilation with \(k = 3\), \(C'=(5\times3,10\times3)=(15,30)\).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(9,15)\) and \((x_2,y_2)=(15,30)\).
\(m=\frac{30 - 15}{15 - 9}\).
\(m=\frac{15}{6}\).
Simplify the fraction: \(m=\frac{5}{2}=2.5\).

Answer:

\(2.5\)