Q. 12 - Geometry

Question

Find the slope and length of AB.

 A(3, -1), B(5, -7)

Step-by-Step Solution

Answer

The slope of the line is -3 and the length of the line is$2\sqrt{10}$ units.

Step-1 – Given

The given points are A(3, -1) and B(5, -7).

Step-2 – To determine

We have to find the slope and the length of the line$\overline{AB}$ .

Step-3 – Calculation

We will use the slope formula with two points$\left(x_1,y_1\right)$ and$\left(x_2,y_2\right)$ : 

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

The given points are A(3, -1) and B(5, -7).

$m=\frac{-7-\left(-1\right)}{\left(5\right)-\left(3\right)}=\frac{-6}{2}=-3$

Length of the line$\overline{AB}$ :

$\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=\sqrt{{\left(5-3\right)}^2+{\left(-7-\left(-1\right)\right)}^2}=2\sqrt{10}$

So, the slope of the line is -3 and the length of the line is$2\sqrt{10}$ units.