Show that the points A a , 0 , B - a , 0 , C 0 , a 3 form an equilateral triangle.

Given vertices of a triangle are A ( a , 0 ) , B ( - a , 0 ) and C ( 0 , a 3 ) . The distance between any two points can be calculated by using the formula d = x 2 - x 1 2 + y 2 - y 1 2 The distance between the points A a , 0 and B - a , 0 is AB = ( - a - a ) 2 + 0 2 ⇒ AB = ( - 2 a ) 2 ⇒ AB = 2 a units The distance between the points B - a , 0 and C 0 , a 3 is BC = ( 0 + a ) 2 + ( 3 a - 0 ) 2 ⇒ BC = ( a ) 2 + 3 a 2 ⇒ BC = 4 a 2 ⇒ BC = 2 a units The distance between the points A a , 0 and C 0 , a 3 ⇒ AC = ( 0 - a ) 2 + ( a 3 - 0 ) 2 ⇒ AC = a 2 + 3 a 2 ⇒ AC = 4 a 2 ⇒ AC = 2 a units So, AB = BC = CA , which means all the sides are equal. Hence, A a , 0 , B - a , 0 , C 0 , a 3 are the vertices of equilateral triangle.

E M B I B E

Mathematics Class 10>Chapter 7 - Coordinate Geometry>Exercise>Q 1

EASY

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IMPORTANT

Earn 100

Find the distance between $(- 2, - 3)$ and $(3, 2)$ .

Important Questions on Coordinate Geometry

EASY

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IMPORTANT

Mathematics Class 10>Chapter 7 - Coordinate Geometry>Exercise>Q 1

Find the distance between

(a, b)

and

(- a, - b)

.

EASY

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IMPORTANT

Mathematics Class 10>Chapter 7 - Coordinate Geometry>Exercise>Q 2

Find the distance between the points

(0, 0)

and

(36, 15)

.

EASY

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IMPORTANT

Mathematics Class 10>Chapter 7 - Coordinate Geometry>Exercise>Q 3

Verify whether the points

(1, 5), (2, 3)

and

(- 2, - 1)

are collinear or not.

MEDIUM

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IMPORTANT

Mathematics Class 10>Chapter 7 - Coordinate Geometry>Exercise>Q 4

Check whether

(5, - 2), (6, 4)

and

(7, - 2)

are the vertices of an isosceles triangle.

HARD

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IMPORTANT

Mathematics Class 10>Chapter 7 - Coordinate Geometry>Exercise>Q 5

In a class room, $4$ friends are seated at the points $A, B, C$ and $D$ as shown in Figure. Jarina and Phani walk into the class and after observing for a few minutes Jarina asks Phani “Don’t you notice that $ABCD$ is a square?” Phani disagrees. Using distance formula, find which of them is correct. Why?
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