The points a - a - a - a and -3 a - -3 a form the vertices of anA- Scalene triangleB- Isosceles Right angled triangleC- Equilateral triangleD- Right angled triangle

The correct option is C Equilateral triangle Let the points be A(a, a), B( a, a), C(–√(3)a, √(3)a) Using distance formula, BC =√((a+√(3)a)^2 + (a √(3)a)^2) ...

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Standard X

Mathematics

Area of a Triangle Given Its Vertices

The points a ...

Question

The points $(a, a)$ , $(- a, - a)$ and $(- \sqrt{3} a, \sqrt{3} a)$ form the vertices of an

Scalene triangle

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Right angled triangle

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Isosceles Right angled triangle

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Equilateral triangle

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Solution

The correct option is D
Equilateral triangle

Let the points be $A (a, a)$ , $B (- a, - a)$ , $C (- \sqrt{3} a, \sqrt{3} a)$

Using distance formula,
$B C = \sqrt{(a + \sqrt{3} a)^{2} + (a - \sqrt{3} a)^{2}} = 2 \sqrt{2} a$
$A B = \sqrt{(a + a)^{2} + (a + a)^{2}} = 2 \sqrt{2} a$
$A C = \sqrt{(- a + \sqrt{3} a)^{2} + (- a - \sqrt{3} a)^{2}} = 2 \sqrt{2} a$

We got $A B = B C = A C = 2 \sqrt{2} a$

$A B C$ is an equilateral triangle

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The points (a,a), (−a,−a) and (–√3a,√3a) form the vertices of an

The correct option is D Equilateral triangle Let the points be A(a,a), B(−a,−a), C(–√3a,√3a) Using distance formula, BC=√(a+√3a)2+(a−√3a)2=2√2a AB=√(a+a)2+(a+a)2=2√2a AC=√(−a+√3a)2+(−a−√3a)2=2√2a We got AB=BC=AC=2√2a ABC is an equilateral triangle

The points $(a, a)$ , $(- a, - a)$ and $(- \sqrt{3} a, \sqrt{3} a)$ form the vertices of an