Question

triangle abc has the points a(1,1), b(7,2) and c(5,7). what composition transformation will result in △abc being at a(2, - 1), b(-4,0) and c(-2,5)? (1 point)

a rotation of - 270 degrees and a move right by 3 and up by 2

a reflction across the y - axis and a move to the left by 5 and up by 3

a refecton across the x - axis and a move to the left by 3 and down by 2

a reflection across the y - axis and a move to the right by 3 and down by 2

a reflection across the y - axis and a move to the right by 3 and down by 2

Explanation:

Step1: Analyze reflection across y - axis rule

The rule for reflecting a point $(x,y)$ across the y - axis is $(x,y)\to(-x,y)$.
For point $A(1,1)$, after reflection across the y - axis, it becomes $(- 1,1)$.
For point $B(7,2)$, after reflection across the y - axis, it becomes $(-7,2)$.
For point $C(5,7)$, after reflection across the y - axis, it becomes $(-5,7)$.

Step2: Analyze translation rule

To get from $(-1,1)$ to $(2,-1)$, we move right by $2-(-1)=3$ units and down by $1 - (-1)=2$ units.
To get from $(-7,2)$ to $(-4,0)$, we move right by $-4-(-7)=3$ units and down by $2 - 0 = 2$ units.
To get from $(-5,7)$ to $(-2,5)$, we move right by $-2-(-5)=3$ units and down by $7 - 5=2$ units.

Answer:

a reflection across the y - axis and a move to the right by 3 and down by 2