Mathematics, 16.12.2019 21:31 judyandaub1

Which point on the y-axis lies on the line that passes through point c and is perpendicular to line ab?
• (-6, 0 )
• ( 0, -6 )
• ( 0, 2 )
• ( 2, 0

Which point on the y-axis lies on the line that passes through point c and is perpendicular to line

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Answer from: Ezonthekid

The line perpendicular to the line AB passes through the point (0,2) i.e., $\fbox{\begin\\\\ \bf option 3\\\end{minispace}}$ .

Further explanation:

From the given figure in the question it is observed that the line AB passes through the points (-2,4) and (2,-8) .

The coordinate for the point C is (6,4) .

Step1: Obtain the slope of the line AB.

The slope of a line which passes through the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$ (1)

It is given that the line AB passes through the points (-2,4) and (2,-8) .

To obtain the slope for the line AB substitute for $x_{1}$ , for $x_{2}$ , for $y_{1}$ and for $y_{2}$ in equation (1).

$\begin{aligned}m&=\frac{-8-4}{2+2}\\&=\frac{-12}{4}\\&=-3\end{aligned}$

Therefore, the slope of the line AB is .

Consider the slope of AB as, $m_{1}$ so, $m_{1}=-3$ .

Step2: Obtain the slope of the perpendicular line.

The slope of line AB is $m_{1}=-3$ .

Consider a line which is perpendicular to the line AB passing through the point C. Assume the slope of the perpendicular line as $m_{2}$ .

The product of slope of two mutually perpendicular lines is always equal to .

The equation formed for the slope is as follows:

$\fbox{\begin\\\ \math m_{1}\times m_{2}=-1\\\end{minispace}}$

Substitute the value of $m_{1}$ in the above equation.

$\begin{aligned}-3\times m_{2}&=-1\\m_{2}&=\frac{1}{3}\end{aligned}$

Therefore, the slope of the perpendicular line is $m_{2}=\frac{1}{3}$ .

Step3: Obtain the equation of the perpendicular line.

The slope for perpendicular line is $\frac{1}{3}$ and the line passes through the point C. The coordinate for the point C are (6,4) .

The point slope form of a line is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$

Substitute $\frac{1}{3}$ for , for $x_{1}$ and for $y_{1}$ in the above equation.

$\begin{aligned}(y-4)&=\frac{1}{3}(x-6)\\3y-12&=x-6\\3y-x&=6\end{aligned}$

Therefore, the equation of the perpendicular line is 3y-x=6 .

Option 1:

In option 1 it is given that the line perpendicular to AB passes through the point (-6,0) .

The equation of the line which is perpendicular to AB is 3y-x=6 .

Substitute for in the above equation.

$\begin{aligned}3y-(-6)&=6\\3y+12&=6\\3y&=-6\\y&=-2\end{aligned}$

From the above calculation it is concluded that the line passes through the point (-6,-2) .

This implies that option 1 is incorrect.

Option 2:

In option 2 it is given that the line perpendicular to AB passes through the point (0,-6) .

The equation of the line which is perpendicular to AB is 3y-x=6 .

Substitute for in the above equation.

$\begin{aligned}3y-(0)&=6\\3y&=6\\y&=2\end{aligned}$

From the above calculation it is concluded that the line passes through the point (0,2) .

This implies that option 2 is incorrect.

Option 3:

In option 3 it is given that the line perpendicular to AB passes through the point (0,2) .

The equation of the line which is perpendicular to AB is 3y-x=6 .

Substitute for in the above equation.

$\begin{aligned}3y-(0)&=6\\3y&=6\\y&=2\end{aligned}$

From the above calculation it is concluded that the line passes through the point (0,2) .

This implies that option 3 is correct.

Option 4:

In option 4 it is given that the line perpendicular to AB passes through the point (2,0) .

The equation of the line which is perpendicular to AB is 3y-x=6 .

Substitute for in the above equation.

$\begin{aligned}3y-(2)&=6\\3y&=8\\y&=\frac{8}{3}\end{aligned}$

From the above calculation it is concluded that the line passes through the point $(2,\frac{8}{3})$ .

This implies that option 4 is incorrect.

Therefore, the line perpendicular to the line AB passes through the point (0,2) i.e., $\fbox{\begin\\\ \bf option 3\\\end{minispace}}$ .

Learn more:

1.A problem on composite function link

2.A problem to find radius and center of circle link

3.A problem to determine intercepts of a line link

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Lines

Keywords: Geometry, coordinate geometry, lines, equation, graph, curve, slope, perpendicular, point slope form, slope intercept form.

Answer from: Quest

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

Answer from: Quest

i don't see any

step-by-step explanation:

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