Maths / Coordinate Geometry / Distance Formula

QUESTION

Prove that the points (4,4),(3,5) and (-1,-1) are the vertices of a right angled triangle.

EXPLANATION
Explain TypeExplanation Content
Text

Let the points (4,4) , (3,5) and (-1,-1) be denoted by P, A and R , respectively.

Now $\large PQ =\sqrt{(3-4)^2+(5-4)^2}=\sqrt{2}$

$\large QR =\sqrt{(-1-3)^2+(-1-5)^2}=\sqrt{52}$

and $\dpi{120} \large PR =\sqrt{(-1-4)^2+(-1-4)^2}=\sqrt{50}$

We observe that the sum of square of two sides , PQ and PR ids equal to the square of the third side QR i.e.,

$QR^2=PR^2+PQ^2$

If follows from the converse of the Pythagoras theorem that the triangle PQR is a right triangle and the right angle is at P.

View Contents
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)
Self Learning
Testimonials
Student Feedback on Methodology - Aman Kumar Shrivastava C/o ABHYAS Academy
10th
One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.

Other Testimonials

Courses We Offer
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)