Q. 13 - Geometry

Question

Find the slope and length of AB.

 A(-3, -2), B(7, -6)

Step-by-Step Solution

Answer

The slope of the line is$-0.4$ and the length of the line is $2\sqrt{41}$units.

Step-1 – Given

The given points are A(-3, -2) and B(7, -6).

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, -2) and B(7, -6).

$m=\frac{-6-\left(-2\right)}{\left(7\right)-\left(-3\right)}=\frac{-4}{10}=-0.4$

Length of the line $\overline{AB}$:

$\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=\sqrt{{\left(7-\left(-3\right)\right)}^2+{\left(-6-\left(-2\right)\right)}^2}=2\sqrt{41}$

So, the slope of the line is$-0.4$ and the length of the line is $2\sqrt{41}$units.