Question

question
what is the image point of (-7, -8) after the transformation ( d_{\frac{1}{2}} circ t_{-1,0} )?
answer attempt 1 out of 2
( , )

Explanation:

Step1: Apply Translation \( T_{-1,0} \)

A translation \( T_{h,k} \) moves a point \( (x,y) \) to \( (x + h, y + k) \). Here, \( h=-1 \), \( k = 0 \), and the point is \( (-7,-8) \). So, \( x'=-7+(-1)=-8 \), \( y'=-8 + 0=-8 \). The point after translation is \( (-8,-8) \).

Step2: Apply Dilation \( D_{\frac{1}{2}} \)

A dilation \( D_{s} \) with scale factor \( s \) transforms a point \( (x,y) \) to \( (s\cdot x, s\cdot y) \). Here, \( s=\frac{1}{2} \), and the point after translation is \( (-8,-8) \). So, \( x''=\frac{1}{2}\times(-8)=-4 \), \( y''=\frac{1}{2}\times(-8)=-4 \).

Answer:

\((-4, -4)\)