Q. 15 - Geometry

Question

Find the slope and length of AB.

 A(0, -9), B(8, -3)

Step-by-Step Solution

Answer

The slope of the line is 0.75 and the length of the line is 10 units.

Step-1 – Given

The given points are A(0, -9) and B(8, -3).

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(0, -9) and B(8, -3).

$m=\frac{\left(-3\right)-\left(-9\right)}{\left(8\right)-\left(0\right)}=\frac{6}{8}=0.75$

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

$\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=\sqrt{{\left(8-\left(0\right)\right)}^2+{\left(-3-\left(-9\right)\right)}^2}=\sqrt{100}=10$

 So, the slope of the line is 0.75 and the length of the line is 10 units.