Question

62. A(4, -1) and B(-2, 3) are points in a coordinate plane. M is the midpoint of AB,What is the length of MB to the nearest tenth of a unit?

Answer 1

The distance between two points A(x1,y1) and B(x2,y2) is given by:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

In this problem we need to find the length of MB which is half AB, therefore the distance will be d/2 or:

`(d)/(2)=\frac{\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}}{2}`

Now, let's replace and solve

x1 = 4

y1 = -1

x2 = -2

y2 = 3

`\begin{gathered} MB=(d)/(2)=\frac{\sqrt[]{(-2-4)^2+\mleft(3+1\mright)^2}}{2} \\ =(1)/(2)\cdot\sqrt[]{(-6)^2+(4)^2} \\ =(1)/(2)\sqrt[]{36+16} \\ =(1)/(2)\sqrt[]{52} \\ =(1)/(2)\cdot2\sqrt[]{13} \\ =\sqrt[]{13} \end{gathered}`

Thus, the length of MB is SQRT(13) or approximately: 3.6