Practice30Create account

A triangle has vertices P(2, −1), Q(6, 2) and R(−4, 7). Which statement about it is correct?

Class 10Coordinate GeometryGeometry — Coordinates
  • AIt is right-angled at Q, with PQ = 5 and QR = 10
  • BIt is isosceles with PQ = PR = 5
  • CIt is right-angled at P, with PQ = 5 and PR = 10
  • DIt is scalene with no right angle

Step-by-Step Solution

; ; . Since , the right angle sits at — the vertex OPPOSITE the longest side . Placing it at is the usual error. The three sides 5, 10 and are all different, so the triangle is scalene AND right-angled.
Answer: C) It is right-angled at P, with PQ = 5 and PR = 10

Key idea: Distance formula

**Distance** between two points P₁, ₁) and Q₂, ₂):

**PQ = **

This is just the Pythagoras theorem applied to the right triangle formed with horizontal and vertical legs.

**Example**: Distance between (3, 4) and (7, 1).
= .

**Special distance from origin**: distance of from (0, 0) is .

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Coordinate Geometry practice questions

More Class 10 Coordinate Geometry practice

The points D(−4, −2), E(2, −2) and F(0, 6) form a triangle. Which description is correct?The points A(−3, 1), B(2, 2), C(4, 6) and D(−1, 5), taken in order, form which…A quadrilateral PQRS has vertices P(3, 0), Q(6, 4), R(11, 4) and S(8, 0). What is the…The vertices of quadrilateral ABCD are A(1, 1), B(5, 3), C(4, 5) and D(0, 3). Using the…Four survey pegs are driven in at A(0, 1), B(4, 4), C(1, 8) and D(−3, 5). Taken in…