Question

1. find the midpoint between each pair of points.

if r is the mid - point of qs, qr = 8x - 51 and rs = 3x - 6, find qs.
qs = 24
qs = 42
qs = 41
qs = 44
clear all

Explanation:

Step1: Set QR equal to RS

Since R is the mid - point of QS, QR = RS. So, $8x−51 = 3x−6$.

Step2: Solve for x

Subtract 3x from both sides: $8x−3x−51=3x−3x - 6$, which simplifies to $5x−51=-6$. Then add 51 to both sides: $5x−51 + 51=-6 + 51$, so $5x = 45$. Divide both sides by 5: $x=\frac{45}{5}=9$.

Step3: Find the length of QR or RS

Substitute x = 9 into the expression for RS (we could also use QR). RS = $3x−6=3\times9−6=27 - 6=21$.

Step4: Find the length of QS

Since QS = QR+RS and QR = RS, QS = 2RS. So QS = $2\times21 = 42$.

Answer:

$QS = 42$