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Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
For the triangle with vertices $A(1,1)$, $B(4,1)$, $C(4,5)$ shown, the side lengths (computed using the distance formula) show that the triangle is:
Equilateral
Isosceles (not right-angled)
Right-angled (a 3-4-5 triangle)
Scalene, no special property
Equilateral
Isosceles (not right-angled)
Right-angled (a 3-4-5 triangle)
Scalene, no special property
Step-by-Step Solution
Key Concept: Compute all three side lengths and check the Pythagorean relation.
$AB=\sqrt{(4-1)^2+0^2}=3$; $BC=\sqrt{0^2+(5-1)^2}=4$; $AC=\sqrt{(4-1)^2+(5-1)^2}=\sqrt{9+16}=5$. [0.5 Mark]
Since $3^2+4^2=5^2$, the triangle is right-angled (with the right angle at $B$). [0.5 Mark]
Since $3^2+4^2=5^2$, the triangle is right-angled (with the right angle at $B$). [0.5 Mark]
Correct Answer: Right-angled (a 3-4-5 triangle)
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