Coordinate Geometry Test

Result

Coordinate Geometry Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

The centroid of a triangle divides the median in the ratio

A
1 : 3

B
3 : 1

C
2 : 1

D
1 : 2

Solution

The centroid of a triangle is the centre of the triangle which is the point of intersection of all the three medians of the triangle and divides the median in the ratio 2 : 1

The median is a line drawn from the mid-point of a side to the opposite vertix
Question 2
1 / -0

The area of the triangle formed by the vertices (x₁,y₁), (x₂,y₂) and (x₃,y₃) is given by

A
2 [x₁(y₂ − y₃) − x₂(y₃− y₁) − x₃(y₁ − y₂)] sq.units

B
1/2 [x₁(y₂ + y₃) − x₂(y₃ + y₁) − x₃(y₁ + y₂)] sq.units

C
1/2 [x₁(y₂ + y₃) + x₂(y₃ + y₁) + x₃(y₁ + y₂)] sq.units

D
1/2 [x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)] sq.units

Solution

The area of the triangle formed by the vertices (x₁,y₁), (x₂,y₂)
and (x₃,y₃) is given by
A = 1/2 [x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)] sq.units
Question 3
1 / -0

Three given points will be collinear, if the area of the triangle formed by these points is

A
0 sq. units

B
1 sq. units

C
2 sq. units

D
– 1 sq. units

Solution

Three points that lie on a same straight line are colinear, and the area of the triangle formed by these collinear points is zero.

Hence Three given points will be collinear, if the area of the triangle formed by these points is 0 sq. units.