Q) Do the points P (1, 0), Q (-5, 0) and R (-2, 5) form a triangle ? If so, name the type of triangle formed.

(Q21 – 30/1/3 – CBSE 2026 Question Paper)

Ans: 

Step 1: Let’s first understand the question:

By Triangle Inequality Property, We know that to form a triangle, the sum of any two sides must be GREATER THAN the third side.

If 3 points do not form a triangle, they will be colinear, and the sum of any two sides must be EQUAL to the third side.

Let’s check if the given points make a triangle or are colinear

Step 2: Let’s start calculating these side length or distances between 2 points one by one:

We know that the Distance Formula, distance between 2 points is given by:

D =

Here, points given are: P (1, 0), Q (-5, 0) and R (-2, 5)

∴ distance between P & Q points, PQ:

=

= = 6 units

Next QR, gap between Q & R points:

Here, points are: Q (-5, 0) and R (-2, 5)

QR =

∴  QR =

= = approx 5.83 units

Next PR, gap between P & R points:

Here, points are: P (1, 0) and R(-2, 5)

PR =

∴ PR  =

= = approx 5.83 units

Step 3: Let’s check if 3 points make a triangle or not:

Here, PQ + QR = 6 + 5.83 = 11.83 and 3rd side is 5.83,

∵ Sum of 2 sides > third side ∴  A triangle is formed

Next, QR + PR = 5.83 + 5.83 = 11.66 and now 3rd side is 6,

∵ Sum of 2 sides > third side => Triangle is formed

Next, PR + PQ = 5.83 + 6 = 11.83 and now 3rd side is 5.83,

∵ Sum of 2 sides > third side => Triangle is formed

Since, in each combination, sum of any two sides is greater than the third,

Therefore, the points P, Q, and R do form a triangle.

Step 4: Let’s find out type of Triangle formed:

In step 2, our calculated sides of the triangle are:

PQ = 6, QR = √34 and PR = √34

Since here two sides are equal (QR = PR),

Therefore, the given points, P, Q and R, form a Isosceles Triangle.

Please press the “Heart”, if you liked the solution.