Question

d is the midpoint of ce. find the length of ce in the diagram below.

diagram shows a line segment ce with d as the mid - point, cd = x + 6 and de = 4x - 21

ce = 30
ce = 9
ce = 5
ce = 15

Explanation:

Step1: Use mid - point property

Since D is the mid - point of CE, then $CD = DE$. So, $x + 6=4x - 21$.

Step2: Solve for x

Subtract x from both sides: $6 = 3x-21$. Then add 21 to both sides: $27 = 3x$. Divide both sides by 3, we get $x = 9$.

Step3: Find length of CE

$CE=CD + DE=(x + 6)+(4x - 21)$. Substitute $x = 9$ into the expression: $CE=(9 + 6)+(4\times9 - 21)=15+(36 - 21)=15 + 15=30$.

Answer:

CE = 30