Question

Suppose Q is the midpoint of PR. Use the information to find the missing value.

PQ= 6x+25 and QR = 16-3x; find PR

Answer 1

Explanation:

If Q is the midpoint of PR

Then PQ + QR = PR

(6x + 25) + (16 - 3x)

group the same terms and add them

(6x - 3x) + (25 + 16)

Hence PR = (3x + 41)

But to find the value of PR....If Q is the midpoint....then PQ = QR...since they are both half lengths of PR;

; 6x + 25 = 16 - 3x

; 6x + 3x = 16 - 25...;9x = -9

Hence the value of...x = -1

Then substitute the value of x into the equation of PR....3x + 41

;3(-1) + 41

;-3 + 41

Hence PR = 38

Answer 2

Answer: PR = 38

Explanation:

Since Q is the midpoint of PR, then PQ = QR

6x + 25 = 16 - 3x

9x + 25 = 16 added 3x to both sides

9x = -9 subtracted 25 from both sides

x = -1 divided both sides by -1

PQ = 6x + 25 QR = 16 - 3x

= 6(-1) + 25 = 16 - 3(-1)

= -6 + 25 = 16 + 3

= 19 = 19

Use the Segment Addition Postulate to find PR:

PR = PQ + QR

= 19 + 19

= 38