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Step-by-step explanation:
Formula for mid-point is;
[tex]midpoint=((x_1+x_2)/2,(y_1+y_2)/2)[/tex]
1.Given S(-3,4), U(-3,0) and T(5,0) then finding the mid-points
SU = [(-3+-3)/2,(4+0)/2] =(-3,2)
TU= [(-3+5)/2,(0+0)/2] =(1,0)
ST=[(-3+5)/2,(4+0)/2]=(1,2)
2.Mid-point formula for this case given W(-5,1) and Z(3,3) will be;
Midpoint = [ (x₁+x₂)/2,(y₁+y₂)/2]
Midpoint= [(-5+3)/2 ,(1+3)/2]
Midpoint=(1,2)
3. Finding the length of segments and the midpoint of the segments
Formula for length of segment, d, is given as;
For C(-1,5) and D(5,1)
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\\\d=\sqrt{(1-5)^2+(5--1)^2}
=\sqrt{-4^2+6^2} =\sqrt{16+36} =\sqrt{52} =7.21[/tex]
Midpoint of the segment CD will be
[(-1+5)/2,(5+1)/2] = (2,3)
For E (-3,-6) and F(5,0)
[tex]d=\sqrt{(0--6)^2+(5--3)^2} =\sqrt{6^2+8^2} =\sqrt{36+64} =\sqrt{100} =10[/tex]
The midpoint for segment EF will be;
[(-3+5)/2 ,(-6+0)/2] =(1,-3)
For L(-4,4) and M(-1,-5)
[tex]d=\sqrt{(-5--4)^2+(-1-4)^2} \\d=\sqrt{-1^2+-5^2} \\\\d=\sqrt{1+25}=\sqrt{26} =5.1[/tex]
Learn More
Midpoint of a segment :https://brainly.com/question/10424143
Distance of a segment :https://brainly.com/question/11591660
Keywords :midpoint, midpoint formula, segment length, line segment
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