Question

multiple choice 1 point
the triangle has been reflected over the line. find x, y and z.
not enough information to determine
x = 2
y = 8
z = 4
x = 1
y = 11
z = 4
x = 1
y = 8
z = 6

Explanation:

Step1: Use reflection property

When a triangle is reflected over a line, corresponding - side lengths are equal. So, we set up the following equations:
For the first pair of corresponding sides: $3z = 12$.
For the second pair of corresponding sides: $2y - 4=18$.
For the third pair of corresponding sides: $9x + 6 = 15$.

Step2: Solve for z

Solve the equation $3z = 12$ for $z$. Divide both sides of the equation by 3:
$z=\frac{12}{3}=4$.

Step3: Solve for y

Solve the equation $2y - 4 = 18$ for $y$. First, add 4 to both sides: $2y=18 + 4=22$. Then divide both sides by 2: $y=\frac{22}{2}=11$.

Step4: Solve for x

Solve the equation $9x + 6 = 15$ for $x$. First, subtract 6 from both sides: $9x=15 - 6 = 9$. Then divide both sides by 9: $x=\frac{9}{9}=1$.

Answer:

$x = 1$
$y = 11$
$z = 4$