Chapter 1.1, Problem 104E

To determine

Find whether the statement is true or false, also give explanations.

Answer to Problem 104E

The statement that is given is false.

Explanation of Solution

Given:

It is given in the question that if the points $(10,-3)$ and $(2,-9)$ lie on the same line then the points $(-12,-\frac{37}{2})$ also lies on that line.

For this, itneeds to find the equation of the line with the first two points.

  $m_1=\frac{-9-(-3)}{2-10}=\frac{-6}{-8}=\frac{3}{4}$

Now, use point slope form,

  $\begin{array}{l}y-(-3)=\frac{3}{4}(x-10)\\ y+3=\frac{3}{4}(x-10)\\ 4y+12=3x-10\\ 4y=3x-10-12\\ y=\frac{3}{4}x-\frac{22}{4}\end{array}$

Now put $(-12,-\frac{37}{2})$ on the above equation if it is zero then it is truw if no then false,

  $\begin{array}{l}y=\frac{3}{4}x-\frac{22}{4}\\ \frac{-37}{2}=\frac{3}{4}\times -12-\frac{22}{4}\\ \frac{-37}{2}=-9-\frac{22}{4}\\ \frac{-37}{2}=\frac{-36-22}{4}\\ \frac{-37}{2}\ne \frac{-58}{4}\end{array}$

So, it is not satisfying so it is false.