Question

1. look at the figure. find the length of $overline{jp}$. 3x - 6 x + 2 h j 6 4 2 8

Explanation:

Step1: Identify equal - sides

Since $\angle H=\angle J$, the triangle $\triangle HPJ$ is isosceles and $HP = JP$. So, set up the equation $3x - 6=x + 2$.
$3x-6=x + 2$

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $3x-x-6=x - x+2$, which simplifies to $2x-6 = 2$. Then add 6 to both sides: $2x-6 + 6=2 + 6$, getting $2x=8$. Divide both sides by 2: $\frac{2x}{2}=\frac{8}{2}$, so $x = 4$.

Step3: Find the length of $\overline{JP}$

Substitute $x = 4$ into the expression for the length of $\overline{JP}$, which is $x + 2$. So, $JP=4 + 2=6$.

Answer:

6