Question

1. if m is the mid - point of (overline{xy}), find the coordinates of x if (m(-3,-1)) and (y(-8,6)). (-3=\frac{-8 + x}{2}) (-1=\frac{6 + y}{2}) 17. if r is the mid - point of (overline{qs}), (qr = 8x-51) and (rs = 3x - 6), find qs. (8x-51 = 3x-6)

Explanation:

Step1: Solve for x - coordinate of X

Solve $-3=\frac{-8 + x}{2}$. Multiply both sides by 2: $-6=-8 + x$. Then $x = 2$.

Step2: Solve for y - coordinate of X

Solve $-1=\frac{6 + y}{2}$. Multiply both sides by 2: $-2=6 + y$. Then $y=-8$.

Step3: Solve for x in QR = RS

Solve $8x - 51=3x - 6$. Subtract $3x$ from both sides: $5x-51=-6$. Add 51 to both sides: $5x = 45$, so $x = 9$.

Step4: Find QS

Since $QS=QR + RS$ and $QR = RS$, $QS = 2RS$. Substitute $x = 9$ into $RS=3x - 6$, $RS=3\times9 - 6=21$. So $QS = 42$.

Answer:

Coordinates of X are $(2,-8)$; $QS = 42$