CBSE Class 10 Mathematics Standard 2024: question 24(b)

Hints

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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.

1. Let $A(3,0)$, $B(6,4)$, $C(-1,3)$. By distance formula, $AB=\sqrt{(6-3{)}^2+(4-0{)}^2}=\sqrt{9+16}=5$

   ½ mark

2. $BC=\sqrt{(6+1{)}^2+(4-3{)}^2}=\sqrt{49+1}=\sqrt{50}$

   ½ mark

3. $CA=\sqrt{(3+1{)}^2+(0-3{)}^2}=\sqrt{16+9}=5$

   ½ mark

4. Since $AB=CA=5$ (two sides equal), $△ABC$ is an isosceles triangle.

   ½ mark

Answer: AB = CA = 5, BC = √50, so the triangle is isosceles.

Revise the chapter

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