Class 9 Exam > Class 9 Questions > Find the coordinates of the point equidistant...
Start Learning for Free
Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).
- a)(2, 3)
- b)(11, 2)
- c)(0, 3)
- d)(1, 3)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find the coordinates of the point equidistant from the points A(1, 2),...
The given three points are A(1,2) B(3,-4) and C(5,-6).
Let P (x, y) be the point equidistant from these three points.
So, PA = PB = PC
⇒ x^2 + 1– 2x + y^2 + 4 – 4y = x^2 + 9 -6x + y^2 + 16 + 8y = x 2 + 25– 10x + y^2 + 36 + 12y
⇒ – 2x– 4y + 5 = -6x + 8y +25= – 10x + 12y+61
– 2x– 4y + 5 = -6x + 8y +25
⇒ – 2x– 4y + 5 +6x - 8y -25=0
⇒ 4x– 12y -20=0
⇒ x– 3y - 5 =0....(i)
- 2x– 4y + 5 = – 10x + 12y+61
⇒- 2x– 4y + 5 +10x - 12y-61=0
⇒8x– 16y -56=0
⇒x– 2y -7=0....(ii)
Solving (i) and (ii)
x = 11, y = 2
Thus, the required point is (11, 2)
Free Test
FREE
| Start Free Test |
Community Answer
Find the coordinates of the point equidistant from the points A(1, 2),...
Finding the Co-ordinates of the Point Equidistant from Three Points
Given Points: A(1, 2), B(3, -4), and C(5, -6)
To find the point equidistant from three points, we need to follow the below steps:
Step 1: Find the Mid-point of AB and BC
- Mid-point of AB = [(1+3)/2, (2-4)/2] = (2,-1)
- Mid-point of BC = [(3+5)/2, (-4-6)/2] = (4,-5)
Step 2: Find the Slope of AB and BC
- Slope of AB = (2-(-4))/(1-3) = 3
- Slope of BC = (-6-(-4))/(5-3) = -1
Step 3: Find the Equation of Perpendicular Bisectors of AB and BC
- Equation of Perpendicular Bisector of AB passing through mid-point (2,-1) with slope m= -1/3 is y+1 = (-1/3)(x-2) i.e. 3y+x=5
- Equation of Perpendicular Bisector of BC passing through mid-point (4,-5) with slope m=1 is y+5 = (1)(x-4) i.e. y=x-9
Step 4: Find the Intersection Point of Both the Perpendicular Bisectors
- Solving the above two equations, we get the intersection point as (11,2)
Therefore, the point equidistant from A, B, and C is (11,2).
Hence, the correct answer is option B.
Given Points: A(1, 2), B(3, -4), and C(5, -6)
To find the point equidistant from three points, we need to follow the below steps:
Step 1: Find the Mid-point of AB and BC
- Mid-point of AB = [(1+3)/2, (2-4)/2] = (2,-1)
- Mid-point of BC = [(3+5)/2, (-4-6)/2] = (4,-5)
Step 2: Find the Slope of AB and BC
- Slope of AB = (2-(-4))/(1-3) = 3
- Slope of BC = (-6-(-4))/(5-3) = -1
Step 3: Find the Equation of Perpendicular Bisectors of AB and BC
- Equation of Perpendicular Bisector of AB passing through mid-point (2,-1) with slope m= -1/3 is y+1 = (-1/3)(x-2) i.e. 3y+x=5
- Equation of Perpendicular Bisector of BC passing through mid-point (4,-5) with slope m=1 is y+5 = (1)(x-4) i.e. y=x-9
Step 4: Find the Intersection Point of Both the Perpendicular Bisectors
- Solving the above two equations, we get the intersection point as (11,2)
Therefore, the point equidistant from A, B, and C is (11,2).
Hence, the correct answer is option B.
|
Explore Courses for Class 9 exam
|
|
Top Courses for Class 9View all
Question Description
Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer?.
Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer?.
Solutions for Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily