PM is a median of Δ PQR with vertices P(5, -6), Q(6, 4) and R(0, 0). The length of PM is: (A) 2√(17) units (B) 2√(15) units (C) √(101) units (D) 10 units

MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 14

From the official CBSE sample question paper for 2026-27, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQCoordinate Geometry

PM is a median of $Δ$ PQR with vertices $P (5, - 6)$ , $Q (6, 4)$ and $R (0, 0)$ . The length of PM is:

(A) $217$ units
(B) $215$ units
(C) $101$ units
(D)10 units

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

A median from P goes to the mid-point of QR.

Hint 2

Apply the distance formula between P and M.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

M is the mid-point of QR: $M = (\frac{6 + 0}{2}, \frac{4 + 0}{2}) = (3, 2)$ .
$P M = (5 - 3)^{2} + (- 6 - 2)^{2} = 4 + 64 = 68 = 217$ units, which is option (A).
1 mark

Answer: $217$ units, option (A)

Where the marks are

Finds M(3, 2) and uses the distance formula to get $217$ (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Applications of the Distance Formula

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2026-27: question 14

Hints

Step-by-step solution

Revise the chapter

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