Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Using the distance formula, show that the given points are col

Question

Using the distance formula, show that the given points are collinear.
$(1, - 1), (5, 2)$ and $(9, 5)$ .

Views: 786 students

Found 6 tutors discussing this question

Evelyn Discussed

Using the distance formula, show that the given points are collinear.

(1, - 1), (5, 2)

and

(9, 5)

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Point are collinear if sum of any two of distances is equal to the distance of the third.

Let

A (1, - 1), B (5, 2), C (9, 5)

A, B and C are collinear if

A B + BC = A C

A B = (5 - 1)^{2} + (2 + 1)^{2} = 4^{2} + 3^{2}

= 16 + 9 = 25 = 5

units

BC = (9 - 5)^{2} + (5 - 2)^{2} = 4^{2} + 3^{2}

= 16 + 9 = 25 = 5

units

A C = (9 - 1)^{2} + (5 + 1)^{2}

= 8^{2} + 6^{2} = 64 + 36 = 100

= 10

units

From above, we can see that

A B + BC = 10 = A C

Therefore A, B and C are collinear.

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Using the distance formula, show that the given points are collinear. $(1, - 1), (5, 2)$ and $(9, 5)$ .
Answer Type	Text solution:1
Upvotes	150