Question

1. triangle lmn with vertices l(2, -8), m(12, 8), and n(14, -4): k = 1/2

l(, )
m(, )
n(, )

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated by a scale - factor $k$, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find the coordinates of $L'$

Given $L(2, - 8)$ and $k=\frac{1}{2}$, then $x'_L=\frac{1}{2}\times2 = 1$ and $y'_L=\frac{1}{2}\times(-8)=-4$. So $L'(1,-4)$.

Step3: Find the coordinates of $M'$

Given $M(12,8)$ and $k = \frac{1}{2}$, then $x'_M=\frac{1}{2}\times12 = 6$ and $y'_M=\frac{1}{2}\times8 = 4$. So $M'(6,4)$.

Step4: Find the coordinates of $N'$

Given $N(14,-4)$ and $k=\frac{1}{2}$, then $x'_N=\frac{1}{2}\times14 = 7$ and $y'_N=\frac{1}{2}\times(-4)=-2$. So $N'(7,-2)$.

Answer:

$L'(1,-4)$
$M'(6,4)$
$N'(7,-2)$