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

Answers: 2

Show answers

Answers

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

Ibelieve the total for the tip could be $21.90

Answer from: Quest

What are the options

Another question on Mathematics

Mathematics, 21.06.2019 15:00

55 bridesmaids want to make 325 325 decorations for a wedding. each decoration takes about 212 2 1 2 minutes to make. which response gives the best estimate for the amount of time each bridesmaid will spend making decorations?

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. x^2 - 20 = x a. 5, 4 b. -5, -4 c. -5, 4 d. 5, -4

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

25 ! i need asap! ! ill mark brainliest!

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

The length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?

Answers: 1

Answer

You know the right answer?

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

Questions

Physics, 17.12.2019 04:31

What force is described as the attraction between a sample of matter and all other matter in the universe?...

Engineering, 17.12.2019 04:31

Place the following statements that describe the 5 steps in an adaptive immune response in the order in which they occur. a. long lived-im...

Business, 17.12.2019 04:31

Sheffield co. both purchases and constructs various equipment it uses in its operations. the following items for two different types of equipment were...

Business, 17.12.2019 04:31

An important application of regression analysis in accounting is in the estimation of cost. by collecting data on volume and cost and using the least...

Chemistry, 17.12.2019 04:31

Animals cannot convert fatty acids into carbohydrates. the net synthesis of one mole of oxaloacetate from two moles of acetyl-coa by the citric acid c...

Business, 17.12.2019 04:31

Steve, the vice president of ocher inc., plans to introduce a retirement plan for all employees. george, the operations director, disagrees because th...

Mathematics, 17.12.2019 04:31

Afactorial experiment was designed to test for any significant differences in the time needed to perform english to foreign language translations with...

Mathematics, 17.12.2019 04:31

It is thought that prehistoric indians did not take their best tools, pottery, and household items when they visited higher elevations for their summe...

Business, 17.12.2019 04:31

For each of the following activities, indicate which of the objectives of managerial accounting activity is involved. in some cases, several objective...

Computers and Technology, 17.12.2019 04:31

On december 1, 2018, keenan company, a u. s. firm, sold merchandise to velez company of canada for 150,000 canadian dollars (cad). collection of the r...

Mathematics, 17.12.2019 04:31

The weekly salary paid to employees of a small company that supplies part-time laborers averages $750 with a standard deviation of $450. (a) if the we...

Biology, 17.12.2019 04:31

Erwin and scott used an insecticidal fog to knock down insects from the top section of a l. seemannii tree. the researchers identified over 900 specie...

Chemistry, 17.12.2019 04:31

These are the components of the reservoirs of carbon that are exchanged in our environment....

Mathematics, 17.12.2019 04:31

In a study undertaken by catalyst, 43% of women senior executives agreed or strongly agreed that a lack of role models was a barrier to their career d...

Computers and Technology, 17.12.2019 04:31

Consider a network with four routers: w, x, y, z. the network includes five links with the following costs: c(x, y)=4, c(x, z)=50, c(y, w)=1, c(z, w...

Biology, 17.12.2019 04:31

What causes the respiratory center in the medulla oblongata...

Mathematics, 17.12.2019 04:31

Light bulbs used for the exterior walkways of a college campus have an average lifetime of 500 hours. assume that the lifetime of bulbs is normally di...

Business, 17.12.2019 04:31

Evaluate the current china/taiwan logistics costs. assume a current total volume of 190,000 cbm and that 89 percent is shipped direct from the supplie...

Physics, 17.12.2019 04:31

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. cars are designed with a "c...

Mathematics, 17.12.2019 04:31

The president of the american insurance institute wants to compare the yearly costs of auto insurance offered by two leading companies. he selects a s...

More questions: Mathematics Another questions

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

Answers

Another question on 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