Question

1. m is the mid - point of. draw a figure to represent this situation, then find pq if = 6 - 7 and = 11 - 2.

Explanation:

Step1: Use mid - point property

Since M is the mid - point of PQ, PM = MQ. Let's assume PM = 6x - 7 and MQ = 11 - 2x. Then 6x - 7=11 - 2x.

Step2: Solve the equation for x

Add 2x to both sides: 6x+2x - 7=11 - 2x+2x, which simplifies to 8x - 7 = 11. Then add 7 to both sides: 8x-7 + 7=11 + 7, so 8x=18. Divide both sides by 8: x=\frac{18}{8}=\frac{9}{4}.

Step3: Find PM or MQ

Substitute x = \frac{9}{4} into PM = 6x - 7. PM=6\times\frac{9}{4}-7=\frac{54}{4}-7=\frac{54 - 28}{4}=\frac{26}{4}=\frac{13}{2}.

Step4: Calculate PQ

Since PQ=PM + MQ and PM = MQ, PQ = 2PM. So PQ = 2\times\frac{13}{2}=13.

Answer:

13