we are building a road that links the points a = (12 ,21) and b =(17,23) another point is in c =(3,9) it is possible that a single road allows to join these three points?

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope ab

we have

a = (12 ,21) and b =(17,23)

substitute

$m=\frac{23-21}{17-12}$

$m=\frac{2}{5}$

step 2

Find the slope ac

we have

a = (12 ,21) and c =(3,9)

substitute

$m=\frac{9-21}{3-12}$

$m=\frac{-12}{-9}$

simplify

$m=\frac{4}{3}$

step 3

Compare slopes ab and ac

The slopes are different

That means ----> is not possible that a single road allows to join these three points

7 0

3 years ago

What is the slope of a line that is perpendicular to the

alexgriva [62]

Answer:

The slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

Step-by-step explanation:

From the line equation, let us take two points

(0, 2)

(4, 1)

Finding the slope between two points

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)$

$m=\frac{1-2}{4-0}$

$m=-\frac{1}{4}$

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be:

$-\frac{1}{-\frac{1}{4}}=4$

Thus, the slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

5 0

3 years ago