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A line has a slope of - 4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Check all that apply.

A(-2,0) and (2,5)
B(-4,5) and (4,-5)
C(-3,4) and (2,0)
D(1,-1) and (6,-5)
E(2,-1) and (10,9)

Verified Answer :

calculista

we know that

if two lines are perpendicular

then the product of their slopes is equal to minus one

so

\(m1*m2=-1\)

in this problem we have

\(m1=-\frac{4}{5}\)

the value of m2 must be equal to

\(m2=-\frac{1}{m1} =-\frac{1}{(-4/5)}=\frac{5}{4}\)

we know that

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

\(m=\frac{(y2-y1)}{(x2-x1)}\)

Find the slopes of each of ordered pairs and compare with m2

case a) \((-2,0)\ and\ (2,5)\)

Substitute in the formula

\(m=\frac{(5-0)}{(2+2)}\)

\(m=\frac{(5)}{(4)}\)

The slope is equal to m2

so

The ordered pair case a)  could be points on a line that is perpendicular to the given  line

case b) \((-4,5)\ and\ (4,-5)\)

Substitute in the formula

\(m=\frac{(-5-5)}{(4+4)}\)

\(m=\frac{(-10)}{(8)}\)

\(m=-\frac{5}{4}\)

The slope is not equal to m2

so

The ordered pair case b)  could not be points on a line that is perpendicular to the given  line

case c) \((-3,4)\ and\ (2,0)\)

Substitute in the formula

\(m=\frac{(0-4)}{(2+3)}\)

\(m=\frac{(-4)}{(5)}\)

The slope is not equal to m2

so

The ordered pair case c)  could not be points on a line that is perpendicular to the given  line

case d) \((1,-1)\ and\ (6,-5)\)

Substitute in the formula

\(m=\frac{(-5+1)}{(6-1)}\)

\(m=\frac{(-4)}{(5)}\)

The slope is not equal to m2

so

The ordered pair case d)  could not be points on a line that is perpendicular to the given  line

case e) \((2,-1)\ and\ (10,9)\)

Substitute in the formula

\(m=\frac{(9+1)}{(10-2)}\)

\(m=\frac{(10)}{(8)}\)

\(m=\frac{5}{4}\)

The slope is equal to m2

so

The ordered pair case e)  could be points on a line that is perpendicular to the given  line

therefore

the answer is

\((-2,0)\ and\ (2,5)\\(2,-1)\ and\ (10,9)\)

The points on the line are:

\(\text{A}. (-2,0) and (2,5)\\\text{E}. (2,1) and (10,9)\)

Step-by-step explanation:

Given information:

The slope of the line = -4/5

Now as we know that the two lines are perpendicular

So,

\(m_1\times m_2=-1\\\)

So, the slope of the second line is :

\(m_2=5/4\)

Now , check for the options given:

And slope \(m= \frac{y_2-y_1}{x_2-x_1}\)

(A) The slope of the line passing through the points (-2,0) and (2,5) is :

\(m=(5-0)/(2+2)\)

\(m=5/4\)

Hence the slope is equal to \(m_2\).

Similarly,

(B)The slope of the line passing through the points (-4,5) and (4,-5) is :

\(m=(-5-5)/(4+4)\)

\(m=-5/4\)

Hence the slope not is equal to \(m_2\).

(C) The slope of the line passing through the points (-3,4) and (2,0) is :

\(m=(0-4)/(2+3)\)

\(m=-4/5\)

Hence the slope is not equal to \(m_2\).

(D) The slope of the line passing through the points (1,-1) and (6,5) is :

\(m=(-5+1)/(6-5)\)

\(m=-4/5\)

Hence the slope is not equal to \(m_2\).

(E) The slope of the line passing through the points (2,-1) and (10,9) is :

\(m=(9+1)/(10-2)\)

\(m=5/4\)

Hence the slope is equal to \(m_2\).

Hence, the points on the lines are:

\(\text{A}. (-2,0) and (2,5)\\\text{E}. (2,1) and (10,9)\)

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