The slope of EF, FG, GH, and HE is 4, -1/4, 4, and -1/4 respectively. And the length of sides EF, FG, GH, and HE will be √68, √68, √68, and √68 units respectively.
What is coordinate geometry?
Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The points E(-4, 6), F(-6, -2), G(2, -4) , and H(4, 4) form quadrilateral EFGH.
Then the slopes are calculated below.
Slope of EF = (6 + 2)/(-4 + 6)
Slope of EF = 8/2
Slope of EF = 4
Slope of FG = (-4 + 2)/(2 + 6)
Slope of FG = -2/8
Slope of FG = -1/4
Slope of GH = (4 + 4)/(4 - 2)
Slope of GH = 8/2
Slope of GH = 4
Slope of HE = (6 - 4)/(-4 - 4)
Slope of HE = -2/8
Slope of HE = -1/4
Then the distance between the point will be
EF² = (-6 + 4)² + (-2 - 6)²
EF² = (-2)² + (-8)²
EF² = 4 + 64
EF = √68
FG² = (2 + 6)² + (-4 + 2)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
GH² = (4 - 2)² + (4 + 4)²
GH² = (2)² + (8)²
GH² = 4 + 64
GH = √68
FG² = (4 + 4)² + (4 - 6)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
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