Question

1. write the rule for a dilation of 5 and a translation of 2 right and 6 up. (x,y) (5x + 2,5y+6) (5(x + 2),5(y + 6)) (5x-2,5y + 6) (5(x - 2),5(y + 6)) clear all

Explanation:

Step1: Apply dilation rule

For a dilation of scale - factor \(k\) in the \(x\) and \(y\) - directions, the rule for a point \((x,y)\) is \((kx,ky)\). Here \(k = 5\), so the point \((x,y)\) becomes \((5x,5y)\) after dilation.

Step2: Apply translation rule

A translation of \(a\) units to the right and \(b\) units up changes the point \((x_1,y_1)\) to \((x_1 + a,y_1 + b)\). After dilation, the point is \((5x,5y)\), and for a translation of \(a = 2\) (right) and \(b = 6\) (up), the new point is \((5x+2,5y + 6)\).

Answer:

\((5x + 2,5y+6)\)