Question

RC is the perpendicular bisector of PQ. PC = 3x - 2 units and QC is equal to 10 units. find x

Answer 1

The diagram shows a triangle bisected by a perpendicular bisector RC. This means the angle PCQ has been divided into two equal halves which are;

`\angle PCR\text{ and }\angle QCR`

Note also that triangle PRC and triangle QRC both have the line segment RC in common.

Then if the line segment RC is a perpendicular bisector of line PQ, it means line segment PR equals RQ.

Therefore, in both triangles PRC and QRC, there is a congruence;

`\begin{gathered} PR=RQ \\ RC=RC \\ \angle PCR=\angle QCR \end{gathered}`

Hence, line PC equals line QC.

We can now et up the following equation.

`\begin{gathered} PC=QC \\ 3x-2=10 \\ \text{Add 2 to both sides;} \\ 3x-2+2=10+2 \\ 3x=12 \\ \text{Divide both sides by 3;} \\ (3x)/(3)=(12)/(3) \\ x=4 \end{gathered}`

ANSWER;

x = 4

The correct answer is option C