Question

Please help I'm stuck on a math problem and please help.Hi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.

Answer 1

We are given a line segment AB with endpoints A(-1. -1) and B(7, 5).

The midpoint of this line segment AB is M with coordinates M(3, 2)

(a) Draw the perpendicular bisector of AB

A perpendicular bisector can be constructed using a compass.

This bisector will be perpendicular (exactly 90°) to the line AB and will pass through the midpoint of line AB.

The bisector drawn above is not drawn to the scale but rather just to give you an idea how it would look like.

The slope of this bisector line and the slope of the line AB will be negative reciprocal of each other.

`m_(BS)=-(1)/(m_(AB))`

Since we are given the endpoints of line AB, we can find its slope as

`m_(AB)=(y_2-y_1)/(x_2-x_1)=(5-(-1))/(7-(-1))=(5+1)/(7+1)=(6)/(8)=(3)/(4)`

So, the slope of the line AB is 3/4.

Then the slope of the perpendicular bisector line will be

`m_(BS)=-(1)/(m_(AB))=-(1)/((3)/(4))=-(4)/(3)`

Therefore, the slope of the perpendicular bisector line is -4/3

(b) Write the equation of the line you drew in (a)

We are asked to find the equation of perpendicular bisector line

We already know its slope and also know that the bisector line passes through point M(3, 2)

Recall that the equation of the line in point-slope form is given by

`(y-y_1)=m(x-x_1)_{}`

Substitute the values of slope and the point into the above equation and solve for y

`\begin{gathered} (y-2_{})=-(4)/(3)(x-3_{})_{} \\ y-2=-(4)/(3)x+(4)/(3)\cdot3_{} \\ y-2=-(4)/(3)x+4_{} \\ y=-(4)/(3)x+4+2 \\ y=-(4)/(3)x+6 \end{gathered}`

Therefore, the equation of the perpendicular bisector line is

`y=-(4)/(3)x+6`