Question

if k is the midpoint of $overline{er}$, ek = x + 5, and er = 4x + 2, what is the length of segment kr? draw and label a diagram, along with showing your solving. x = kr =

Explanation:

Step1: Use mid - point property

Since K is the mid - point of $\overline{ER}$, we know that $EK = KR$ and $ER=2EK$. So, $4x + 2=2(x + 5)$.

Step2: Solve the equation for x

Expand the right - hand side: $4x+2 = 2x+10$. Subtract $2x$ from both sides: $4x - 2x+2=2x - 2x + 10$, which gives $2x+2 = 10$. Then subtract 2 from both sides: $2x+2 - 2=10 - 2$, so $2x=8$. Divide both sides by 2: $x = 4$.

Step3: Find the length of KR

Since $KR = EK=x + 5$, substitute $x = 4$ into the expression for $EK$. Then $KR=4 + 5=9$.

Answer:

$x = 4$
$KR = 9$