Q. 14 - Geometry

Question

Find the slope and length of AB.

14. A(8, -7), B(-3, -5)

Step-by-Step Solution

Answer

The slope of the line is$-0.18$ and the length of the line is$5\sqrt{5}$ units.

Step-1 – Given

The given points are A(8, -7) and B(-3, -5).

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(8, -7) and B(-3, -5).

$m=\frac{\left(-5\right)-\left(-7\right)}{\left(-3\right)-\left(8\right)}=\frac{2}{-11}=-0.18$

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

$\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=\sqrt{{\left(-5-\left(-7\right)\right)}^2+{\left(-3-\left(8\right)\right)}^2}=\sqrt{125}=5\sqrt{5}$

 So, the slope of the line is$-0.18$ and the length of the line is $5\sqrt{5}$units.