Question

triangle pqr has coordinates p(-1, 5), q(1, 2), and r(-3, -1). determine the coordinates of the vertices of the image after a translation along the vector < 5, -4 >.

a) p(1, 5), q(-1, 2), and r(3, -1)
b) p(-6, 9), q(-4, 6), and r(-8, 3)
c) p(4, 1), q(6, -2), and r(2, -5)
d) p(-5, -20), q(5, -8), and r(15, 4)

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Explanation:

Step1: Recall translation rule

To translate a point $(x,y)$ along the vector $\langle a,b
angle$, the new - coordinates are $(x + a,y + b)$.

Step2: Translate point P

For point $P(-1,5)$ and vector $\langle5,-4
angle$, the new $x$ - coordinate is $-1+5 = 4$ and the new $y$ - coordinate is $5+( - 4)=1$. So the new coordinates of $P$ are $(4,1)$.

Step3: Translate point Q

For point $Q(1,2)$ and vector $\langle5,-4
angle$, the new $x$ - coordinate is $1 + 5=6$ and the new $y$ - coordinate is $2+( - 4)=-2$. So the new coordinates of $Q$ are $(6,-2)$.

Step4: Translate point R

For point $R(-3,-1)$ and vector $\langle5,-4
angle$, the new $x$ - coordinate is $-3 + 5 = 2$ and the new $y$ - coordinate is $-1+( - 4)=-5$. So the new coordinates of $R$ are $(2,-5)$.

Answer:

C. $P(4,1),Q(6,-2),$ and $R(2,-5)$