Question

points w, x, and y are collinear. point x is between w and y, wy = 9x - 21, wx = 6x + 9, and xy = x. find wx, xy, and wy. wx =

Explanation:

Step1: Set up equation

Since W, X, Y are collinear and X is between W and Y, we have WY = WX + XY. Substituting the given expressions, we get the equation $9x - 21=(6x + 9)+x$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(6x + 9)+x=7x + 9$. So the equation becomes $9x - 21=7x + 9$.

Step3: Solve for x

Subtract $7x$ from both sides: $9x-7x - 21=7x-7x + 9$, which simplifies to $2x-21 = 9$. Then add 21 to both sides: $2x-21 + 21=9 + 21$, so $2x=30$. Divide both sides by 2: $x = 15$.

Step4: Find WX

Substitute $x = 15$ into the expression for WX. WX=$6x + 9=6\times15+9=90 + 9=99$.

Step5: Find XY

Substitute $x = 15$ into the expression for XY. XY=$x = 15$.

Step6: Find WY

Substitute $x = 15$ into the expression for WY. WY=$9x - 21=9\times15-21=135-21 = 114$.

Answer:

WX = 99, XY = 15, WY = 114