Question

graph $\triangle jkl$ with vertices $j(1,3)$, $k(5,0)$, and $l(7,4)$ and its image after the glide reflection with a translation along $<-3,0>$ and a reflection in the $x$-axis.

Explanation:

Step1: Translate the triangle

To translate a point \((x,y)\) along the vector \(\langle - 3,0
angle\), we use the rule \((x,y)\to(x - 3,y)\).
For point \(J(1,3)\): \(J'(1-3,3)=J'(-2,3)\)
For point \(K(5,0)\): \(K'(5 - 3,0)=K'(2,0)\)
For point \(L(7,4)\): \(L'(7-3,4)=L'(4,4)\)

Step2: Reflect the translated triangle in the \(x\) - axis

To reflect a point \((x,y)\) in the \(x\) - axis, we use the rule \((x,y)\to(x,-y)\)
For point \(J'(-2,3)\): \(J''(-2,-3)\)
For point \(K'(2,0)\): \(K''(2,0)\)
For point \(L'(4,4)\): \(L''(4,-4)\)

Answer:

The vertices of the original triangle \(\triangle JKL\) are \(J(1,3)\), \(K(5,0)\), \(L(7,4)\). The vertices of the translated triangle (after translation along \(\langle - 3,0
angle\)) are \(J'(-2,3)\), \(K'(2,0)\), \(L'(4,4)\). The vertices of the final image (after reflection in the \(x\) - axis) are \(J''(-2,-3)\), \(K''(2,0)\), \(L''(4,-4)\). To graph:

• Plot \(J(1,3)\), \(K(5,0)\), \(L(7,4)\) for \(\triangle JKL\).
• Plot \(J'(-2,3)\), \(K'(2,0)\), \(L'(4,4)\) for the translated triangle.
• Plot \(J''(-2,-3)\), \(K''(2,0)\), \(L''(4,-4)\) for the glide - reflected triangle.