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Given U(1,-9), V(5,7), W(-8,-1),U(1,−9),V(5,7),W(−8,−1), and X(x, 7).X(x,7). Find xx such that UV∥ WX.

1 Answer

4 votes

Answer:

x = -6

Explanation:

You want the x-coordinate of point X(x, 7) such that line WX is parallel to line UV when the points are U(1, -9), V(5, 7), W(-8, -1).

Graph

It works fairly nicely to graph the given points. This lets you see that line UV has a rise/run of 4/1. You can find the desired point by drawing a line through W with the same slope. It crosses the horizontal line y=7 at x = -6.

The point of interest is X(-6, 7), where x = -6.

Equations

The slope of UV is ...

m = (y2 -y1)/(x2 -x1)

m = (7 -(-9))/(5 -1) = 16/4 = 4

Then the point-slope equation of the line through W is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

y -(-1) = 4(x -(-8)

Solving for x gives ...

(y +1)/4 -8 = x

(7 +1)/4 -8 = x = -6 . . . . . . . for point (x, 7)

The x-coordinate of point X is -6.

<95141404393>

Given U(1,-9), V(5,7), W(-8,-1),U(1,−9),V(5,7),W(−8,−1), and X(x, 7).X(x,7). Find-example-1
User Raphaeltm
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