The length of the line in graph is the difference of the two points of the coordinates. AB to the nearest tenth is 7 units and the coordinates of the midpoint of AB is [tex]\left ( 0.5, -4 \right )[/tex].
Given information-
The points of the line given in the graph are (4,-5) and (-3,-3).
a) The length of the AB.
Length of the line-
The length of the line in graph is the difference of the two points of the coordinates.
The length [tex]d[/tex] of line with points [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] can be given as,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(-3-4)^2+(-3-(-5))^2}[/tex]'
[tex]d=\sqrt{(-7)^2+(2)^2}[/tex]
[tex]d=\sqrt{(49+4)}[/tex]
[tex]d=\sqrt{53}[/tex]
[tex]d=7.28[/tex]
The length of the line AB to the nearest tenth is 7 units.
b) the coordinates of the midpoint of AB.
The coordinates [tex](x,y)[/tex] of the midpoint of a line with points [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] can be given as,
[tex](x,y)=\left ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2} \right )[/tex]
[tex](x,y)=\left ( \dfrac{4-3}{2}, \dfrac{-5-3}{2} \right )[/tex]
[tex](x,y)=\left ( \dfrac{1}{2}, \dfrac{-8}{2} \right )[/tex]
[tex](x,y)=\left ( 0.5, -4 \right )[/tex]
Hence the length of the line AB to the nearest tenth is 7 units and the coordinates of the midpoint of AB is [tex]\left ( 0.5, -4 \right )[/tex].
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