Question

1. the vertices of △abc are a(-1,8), b(-6,10), c(-8,5). translations on a coordinate plane graph △abc and △abc, its image, after a translation of 8 units to the right and 6 units down. use arrow notation to show how each vertex of △abc maps to its image, then write an algebraic rule for the translation. translation rule: (x,y)→( , ) a(-1,8)→a( ) b(-6,10)→b( ) c(-8,5)→c( )

Explanation:

Step1: Determine the translation rule

For a translation of 8 units to the right and 6 units down, the algebraic rule for a point $(x,y)$ is $(x,y)\to(x + 8,y-6)$.

Step2: Find the coordinates of $A'$

Given $A(-1,8)$, using the rule $(x,y)\to(x + 8,y - 6)$, we have $x=-1$ and $y = 8$. Then $x+8=-1 + 8=7$ and $y-6=8-6 = 2$. So $A'=(7,2)$.

Step3: Find the coordinates of $B'$

Given $B(-6,10)$, with $x=-6$ and $y = 10$. Then $x + 8=-6+8 = 2$ and $y-6=10 - 6=4$. So $B'=(2,4)$.

Step4: Find the coordinates of $C'$

Given $C(-8,5)$, with $x=-8$ and $y = 5$. Then $x+8=-8 + 8=0$ and $y-6=5-6=-1$. So $C'=(0,-1)$.

Answer:

The translation rule is $(x,y)\to(x + 8,y-6)$, $A'=(7,2)$, $B'=(2,4)$, $C'=(0,-1)$