Question

points w, x, and y are collinear. point x is between w and y, wy = 20x, wx = 6x + 10, and xy = 8x + 8. find xy.

Explanation:

Step1: Use collinear - point property

Since W, X, Y are collinear and X is between W and Y, we have $WX + XY=WY$.
Substitute the given expressions: $(6x + 10)+(8x + 8)=20x$.

Step2: Simplify the left - hand side

Combine like terms: $6x+8x + 10 + 8=20x$, which gives $14x+18 = 20x$.

Step3: Solve for x

Subtract $14x$ from both sides: $18=20x - 14x$, so $18 = 6x$.
Divide both sides by 6: $x=\frac{18}{6}=3$.

Step4: Find XY

Substitute $x = 3$ into the expression for $XY$: $XY=8x + 8$.
$XY=8\times3+8=24 + 8=40$.

Answer:

40