Q. 25 - Geometry

Question

 A line with slope m passes through points (p, q) and (r, ?). 

Step-by-Step Solution

Answer

A line with slope$m$  passes through points$\left(p,q\right)\text{ and }\left(r,mr-mp+q\right)$ 

Step-1 – Given

A line with slope $m$ passes through points$\left(p,q\right)\text{ and }\left(r,?\right)$ 

Step-2 – To determine

We have to find the unknown y coordinate of the given point.

Step-3 – Calculation

The slope formula for two points$\left(x_1,y_1\right)$ and$\left(x_2,y_2\right)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

The given points are $\left(p,q\right)\text{ and }\left(r,?\right)$.

Let = the unknown x coordinate

So,

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{y_2-q}{r-p}\\ y_2-q=m\left(r-p\right)\\ y_2=m\left(r-p\right)+q\\ y_2=mr-mp+q\end{array}$

Hence, the unknown y coordinate is $mr-mp+q$.