Chapter 3.6, Problem 38PPS

(a)

To determine

To Graph:The segments.

Explanation of Solution

Given: $AB$ has a slope of $2$ and midpoint $M(3,2)$ . A segment perpendicular to $AB$ has midpoint $P(4,-1)$ and shares end point $B$ with $AB$ .

Using midpoint $M(3,2)$ .

The slope of the line is $2$ thus moving the points $2$ units up then one unit to the right.

We obtain the point $(4,4)$ and named the point as $A.$

Using midpoint $P(4,-1)$ .

The slope of the line is $2$ thus moving the points $2$ units up then one unit to the left.

We obtain the point $(2,0)$ and named the point as $B.$

The graph is shown below.

  

(b)

To determine

To Find: The coordinates of $AandB.$

Answer to Problem 38PPS

  $\begin{array}{l}A=(4,4)\\ B=(2,0)\end{array}$

Explanation of Solution

Given: $AB$ has a slope of $2$ and midpoint $M(3,2)$ . A segment perpendicular to $AB$ has midpoint $P(4,-1)$ and shares end point $B$ with $AB$ .

From part (a) the coordinates are

  $\begin{array}{l}A=(4,4)\\ B=(2,0)\end{array}$