Question #221070

Find the midpoint and distance of the line segment that connects the following points a) (0,3) and (4,7) b) (-9,6) and (-1, -2) c) (-4.5, -12.5) and (4.5, 13)


1
Expert's answer
2021-08-01T09:37:18-0400

The mid point of line segment joining two points ( x1, y1 ) and ( x2, y2 ) is given by


(x,y)=x1+x22,y1+y22(x, y) = \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}



and the distance between two points is given by


d=(x2x1)2+(y2y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}



a) (0,3) and (4,7)


mid point (x,y)=0+42,3+72(x, y) = \dfrac{0+4}{2}, \dfrac{3+7}{2}



mid point (x,y)=(2, 5)(x, y) = (2,\ 5)




d=(40)2+(73)2d = \sqrt{(4-0)^2+(7-3)^2}


d=42 unitsd = 4\sqrt{2} \ units





b) (-9,6) and (-1, -2)


mid point (x,y)=912,622(x, y) = \dfrac{-9-1}{2}, \dfrac{6-2}{2}



mid point (x,y)=(5, 2)(x, y) = (-5,\ 2)




d=(1+9)2+(26)2d = \sqrt{(-1+9)^2+(-2-6)^2}


d=82 unitsd = 8\sqrt{2} \ units









c) (-4.5, -12.5) and (4.5, 13)


mid point (x,y)=4.5+4.52,12.5+132(x, y) = \dfrac{-4.5+4.5}{2}, \dfrac{-12.5+13}{2}



mid point (x,y)=(0, 0.25)(x, y) = (0,\ 0.25)




d=(4.5+4.5)2+(13+12.5)2d = \sqrt{(4.5+4.5)^2+(13+12.5)^2}


d=27.04 unitsd = 27.04 \ units

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