Question

use the figure above square abcd to answer the following what is the slope m of ab and bc ? what is point d to make this square?

Answer 1

Answer

Slope of line AB = (3/2) OR 1.5

Slope of line BC = (-2/3)

Point D = (0, 6)

Explanation

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

$Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}$

For line AB, we will use points A and B to calculate the slope.

(x₁, y₁) and (x₂, y₂) are (6, 2) and (2, -4)

$\text{Slope = }\frac{-4-2}{2-6}=\frac{-6}{-4}=\frac{3}{2}=1.5$

For line BC, we will use points B and C to calcuate the slope.

(x₁, y₁) and (x₂, y₂) are (2, -4) and (-4, 0)

$\text{Slope = }\frac{0-(-4)}{-4-2}=\frac{0+4}{-6}=\frac{4}{-6}=-\frac{2}{3}$

So, for the next part, we need to pick a point D that will make this structure a square

This point D, from point C has to spread 6 units over the y-axis and 4 units over the x-axis.

This leads us to

(-4 + 4, 0 + 6) = (0, 6)

Point D = (0, 6)

Hope this Helps!!!