Question 161979
Well, for a person who doesn't know how to do this, you sure got the right answer!
Let's first find the mid-point of the line segment DE.
D(4,2) and E(-8,18)
The coordinates of the mid-point of a line segment are given by:
({{{(x[1]+x[2])/2}}},{{{(y[1]+y[2])/2}}}) making the appropriate substitutions:
({{{(4+(-8))/2}}},{{{(2+18)/2}}}) Simplify.
({{{-4/2}}},{{{20/2}}})
({{{-2}}},{{{10}}})
Now we find the slope (m) of the line segment from C(2,2) to the mid-point of DE(-2,10) using the slope formula:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} making the appropriate substitutions:
{{{m = (10-2)/(-2-2)}}} Simplify.
{{{m = 8/-4}}}
{{{m = -2}}}
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Well, UV = the sum of the two equal halves UY+YV and UY = 4x-3 and YV = x, so...
UV = (4x-3)+x
UV = 5x-3
So you are correct on both problems!