Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 30, 2023

Find the equation of the line containing side $\overline{\mathrm{BP}}$ in a parallelogram where the opposite sides have the same slope, given the equation of the line containing side $\overline{\mathrm{DQ}}$ is $y-7=5(x+4)$ .

STEP 1

Assumptions1. The opposite sides of a parallelogram have the same slope. . The equation of the line containing side $\overline{\mathrm{Q}}$ is $y-7=5(x+4)$ .
3. We need to find the equation of the line containing side $\overline{\mathrm{BP}}$ in point-slope form.

STEP 2

The slope of the line containing side $\overline{\mathrm{Q}}$ can be found from its equation. The equation $y-7=5(x+4)$ is in point-slope form, $y-y1=m(x-x1)$ , where $m$ is the slope.
So, the slope of $\overline{\mathrm{Q}}$ is $5$ .

STEP 3

Since the opposite sides of a parallelogram have the same slope, the slope of $\overline{\mathrm{BP}}$ is also $5$ .

STEP 4

We don't know the coordinates of point B, but we can represent them as $(x1,y1)$ .

STEP 5

Now we can write the equation of the line containing side $\overline{\mathrm{BP}}$ in point-slope form using the slope we found and the coordinates of point B.
$y-y1=5(x-x1)$ This is the equation of the line containing side $\overline{\mathrm{BP}}$ in point-slope form.

Was this helpful?

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Contact Influencer program Policy Terms