Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Prove, using the distance formula, that the points $(3,0)$, $(6,4)$, $(-1,3)$ are the vertices of a right isosceles triangle.
Step-by-Step Solution
Key Concept: Compute all three sides; check two are equal (isosceles) and the Pythagorean relation holds (right-angled).
$AB=\sqrt{9+16}=5$; $BC=\sqrt{49+1}=\sqrt{50}$; $AC=\sqrt{16+9}=5$. [1.5 Marks]
Since $AB=AC=5$, the triangle is isosceles. [0.5 Mark]
Also $AB^2+AC^2=25+25=50=BC^2$, so the triangle is right-angled at $A$. Hence $ABC$ is a right isosceles triangle. [1.0 Mark]
Correct Answer:
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