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
Nady [450]
3 years ago
10

Calculate pt3 such that a line from pt1 to pt3 is perpendicular to the line from pt1 to pt2, and the distance between pt1 and pt

2 is the same as the distance between pt1 and pt3 *
Mathematics
1 answer:
Leni [432]3 years ago
8 0
Let the point_1 = p₁ = (1,4)
and      point_2 = p₂ = (-2,1)
and      Point_3 = p₃ = (x,y)

The line from point_1 to point_2 is L₁ and has slope = m₁
The line from point_1 to point_3 is L₂ and has slope = m₂
m₁ = Δy/Δx = (1-4)/(-2-1) = 1
m₂ = Δy/Δx = (y-4)/(x-1)
L₁⊥L₂ ⇒⇒⇒⇒ m₁ * m₂ = -1
∴ (y-4)/(x-1) = -1 ⇒⇒⇒ (y-4)= -(x-1)
(y-4) = (1-x) ⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒ equation (1)

The distance from point_1 to point_2 is d₁
The distance from point_1 to point_3 is d₂
d = \sqrt{Δx^2+Δy^2}
d₁ = \sqrt{(-2-1)^2+(1-4)^2}
d₂ = \sqrt{(x-1)^2+(y-4)^2}
d₁ = d₂
∴ \sqrt{(-2-1)^2+(1-4)^2} = \sqrt{(x-1)^2+(y-4)^2} ⇒⇒ eliminating the root
∴(-2-1)²+(1-4)² = (x-1)²+(y-4)²
 (x-1)²+(y-4)² = 18
from equatoin (1)  y-4 = 1-x
∴(x-1)²+(1-x)² = 18            ⇒⇒⇒⇒⇒ note: (1-x)² = (x-1)²
2 (x-1)² = 18
(x-1)² = 9
x-1 = \pm \sqrt{9} = \pm 3
∴ x = 4 or x = -2
∴ y = 1 or y = 7

Point_3 = (4,1)  or  (-2,7)












You might be interested in
Easy points!!!
Softa [21]

Answer:

51, 52, 53

Step-by-step explanation:

51, 52, and 53 are all greater than 50, but less than 54

7 0
2 years ago
Eric's water bottle holds 500 mL. He drinks 4 bottles of water at soccer practice.
nalin [4]

2 litres of water. A

4 0
3 years ago
Read 2 more answers
Perform the following calculation. Express your answer in scientific notation. (2×105) + (6×105) Write your answer in scientific
ZanzabumX [31]
Answer:

8.4x10^1
Thanks
7 0
3 years ago
Read 2 more answers
The force which pulls or tends to pull a body is called____​
Setler [38]

Answer:

force of gravity

hope it helps

pls mark me as the brainliest

thank u

8 0
2 years ago
Read 2 more answers
You roll a fair 6-sided die . what is the probability of rolling a 2 .
Lynna [10]

Answer:

P = 1/6

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the equation for a slope of -3 and y intercept of 7
    11·1 answer
  • The mouse weights​ (in grams) of a random sample of 100 mice involved in a nutrition experiment​ are: Interval 41.5----43.5 43.5
    10·1 answer
  • Pls help 10 pts t the first person
    12·1 answer
  • Chris is standing due south of a 20m flagpole at a point where the angle of elevation of the top of the pole is 35. Brandyn is s
    12·1 answer
  • A box of cereal has a width of 4 inches, and a length of 8 inches and a height of 12 inches. What is the volume of the box, in c
    14·1 answer
  • Write an equation in slope intercept form for the line with slope -1/5and y intercept -7
    13·2 answers
  • BRAINLIEST FOR CORRECT ANSWER, IM FAILING SCHOOL AND NEED HELP ASAP. EVEN OFFICIAL HELP COUNTS
    8·2 answers
  • MARKING BRAINLIEST
    12·2 answers
  • Select all of the following expressions that are equivalent to 9 to the 1/2 power
    12·1 answer
  • Find all solutions to the equation.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!