1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mars2501 [29]
2 years ago
6

Part B

Mathematics
1 answer:
alisha [4.7K]2 years ago
3 0

Question:

Consider ΔABC, whose vertices are A (2, 1), B (3, 3), and C (1, 6); let the line segment  AC represent the base of the triangle.

(a)  Find the equation of the line passing through B and perpendicular to the line AC

(b)  Let the point of intersection of line AC with the line you found in part A be point D. Find the coordinates of point D.

Answer:

y = \frac{1}{5}x + \frac{12}{5}

D = (\frac{43}{26},\frac{71}{26})

Step-by-step explanation:

Given

\triangle ABC

A = (2,1)

B = (3,3)

C = (1,6)

Solving (a): Line that passes through B, perpendicular to AC.

First, calculate the slope of AC

m = \frac{y_2 - y_1}{x_2 - x_1}

Where:

A = (2,1) --- (x_1,y_1)

C = (1,6) --- (x_2,y_2)

The slope is:

m = \frac{6- 1}{1 - 2}

m = \frac{5}{-1}

m = -5

The slope of the line that passes through B is calculated as:

m_2 = -\frac{1}{m} --- because it is perpendicular to AC.

So, we have:

m_2 = -\frac{1}{-5}

m_2 = \frac{1}{5}

The equation of the line is the calculated using:

m_2 = \frac{y_2 - y_1}{x_2 - x_1}

Where:

m_2 = \frac{1}{5}

B = (3,3) --- (x_1,y_1)

(x_2,y_2) = (x,y)

So, we have:

\frac{1}{5} = \frac{y - 3}{x - 3}

Cross multiply

5(y-3) = 1(x - 3)

5y - 15 = x - 3

5y  = x - 3 + 15

5y  = x +12

Make y the subject

y = \frac{1}{5}x + \frac{12}{5}

Solving (b): Point of intersection between AC and y = \frac{1}{5}x + \frac{12}{5}

First, calculate the equation of AC using:

y = m(x - x_1) + y_1

Where:

A = (2,1) --- (x_1,y_1)

m = -5

So:

y=-5(x - 2) + 1

y=-5x + 10 + 1

y=-5x + 11

So, we have:

y=-5x + 11 and y = \frac{1}{5}x + \frac{12}{5}

Equate both to solve for x

i.e.

y = y

-5x + 11 = \frac{1}{5}x + \frac{12}{5}

Collect like terms

-5x -\frac{1}{5}x = \frac{12}{5} - 11

Multiply through by 5

-25x-x = 12 - 55

Collect like terms

-26x = -43

Solve for x

x = \frac{-43}{-26}

x = \frac{43}{26}

Substitute x = \frac{43}{26} in y=-5x + 11

y = -5 * \frac{43}{26} + 11

y =  \frac{-5 *43}{26} + 11

Take LCM

y =  \frac{-5 *43+11 * 26}{26}

y =  \frac{71}{26}

Hence, the coordinates of D is:

D = (\frac{43}{26},\frac{71}{26})

You might be interested in
explain why there is never a single correct answer to a question that asks you to estimate some quantity
motikmotik
Because others would estimate it differently. 
7 0
3 years ago
In ΔLMN, \overline{LN} LN is extended through point N to point O, m∠NLM = (x+1)^{\circ}(x+1) ∘ , m∠LMN = (x+15)^{\circ}(x+15) ∘
mixer [17]

Answer:

26 degree

Step-by-step explanation:

We are given that  in triangle

\angle NLM=(x+1)^{\circ}

\angke LMN=(x+15)^{\circ}

\angle MNO=(4x+6)^{\circ}

\angle MNO+\angle MNL=180^{\circ}

By using linear pair angles property

\angle MNL=180-\angle MNO=180-(4x+6)

\angle MNL+\angle NLM+\angle LMN=180^{\circ}

By using triangle angles sum property

180-(4x+6)+x+15+x+1=180

2x+16=180-180+4x+6

16-6=4x-2x=2x

2x=10

x=\frac{10}{2}=5

Substitute the value

\angle MNO=4(5)+6=20+6=26^{\circ}

3 0
3 years ago
Monday's temperature was 6 degree the low temperature was -3 degree what was the difference between the high and low temperature
maw [93]
The <span>the difference between the high and low temperatures was 9 degrees. </span>
8 0
3 years ago
Read 2 more answers
Prior to hosting an international soccer match, the local soccer club needs to replace the artificial turf on their field with g
r-ruslan [8.4K]

Answer:

$44,313.75

Step-by-step explanation:

First, we need to turn the km into meters. There are 1000 meters in a km meaning we need to multiply each of these values by 1000.

0.101 km * 1000= 101 meters

0.065 km * 1000 =  65 meters

Now we need to multiply these values together to find the area of the field

101m * 65m = 6,565m^{2}

Finally, we need to multiply this area by the cost per square meter

6,565m^{2} / 6.75 = $44,313.75

The total repair will cost $44,313.75

3 0
3 years ago
16 = d - 12 / 14 <br> what is the answer?
Aleonysh [2.5K]

Answer:

16=d-12/14

We simplify the equation to the form, which is simple to understand  

16=d-12/14

Simplifying:

16=d-0.857142857143

We move all terms containing d to the left and all other terms to the right.  

-1d=-0.857142857143-16

We simplify left and right side of the equation.  

-1d=-16.8571428571

We divide both sides of the equation by -01 to get d.  

d=16.8571428571

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • 8. Albert's father is 24 years older than Albert is. In 8 years, his father will be twice as old as Albert. How old is Albert no
    9·1 answer
  • Please help me !!!!!!!!
    12·1 answer
  • What is the sum of -2 and -7?
    14·2 answers
  • Which categories does 11 belong in
    15·1 answer
  • Determine the perimeter of a equilateral triangle with the sides of 28 cm.
    15·1 answer
  • Angelique has a bag that contains six red marbles and four blue marbles and 14 yellow marbles if she chooses one marble from the
    11·1 answer
  • IT’S TIMED NEED HELP ASAP! Write the relationship between the sides for these two congruent triangles.
    8·1 answer
  • I need help, I’ve been stuck on this question plz
    15·1 answer
  • On a coordinate plane, triangle G H J has points (1, 1), (4, 1), (4, 5).
    14·1 answer
  • What is the point-slope form of the line with slope 2/5 that passes through the point (-4, -7) ?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!