Mathematics: 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

It would be considered a mixed number...

Which point on the y-axis lies on the line that

Ответ:

shsbbdDnsgs3913

12.01.2022

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.

0,0(0 оценок)

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

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question