Class 10 : math lesson 7 Coordinate Geometry free online test and quiz : online mcq test for class 10 math

Coordinate Geometry online mcq quiz

Coordinate Geometry boostup points 

➦ Distance formula

 •  The distance between the points P (x1, y1) and Q (x2, y2) is given byPQ=x2-x12+y2-y12

• The distance of a point (x, y) from the origin O (0, 0) is given by OP=x2+y2 .

➦ Section formula:

The co-ordinates of the point P (x,y), which divides the line segment joining the points A (x1, y1) and B (x2, y2) internally in the ratio m:n, are given by:P x, y=mx2+nx1m+n, my2+ny1m+n

•  The mid-point of the line segment joining the points A (x1, y1) and B (x2, y2) is x1+x22, y1+y22 . [Note: Here, m = n = 1]

• If A (x1, y1), B (x2, y2) and C (x3, y3) are the vertices of ΔABC, then the coordinates of 

its centroid are given by the point x1+x2+x33, y1+y2+y33

➦ Area of a triangle

The area of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) is given by 

the numerical value of the expression 12x1y2-y3+x2y3-y1+x3y1-y2

Example 1:Find the area of the triangle whose vertices are P (–2, 2), Q (2, 0) and R (8, 5).

Solution:

We have P (–2, 2), Q (2, 0) and R (8, 5) as the given points.

Let (x1, y1) = (–2, 2); (x2, y2) = (2, 0); (x3, y3) = (8, 5)

area of ∆PQR = 12x1y2-y3+x2y3-y1+x3y1-y2⇒area of ∆PQR = 12-20-5+25- 2+82-0⇒area of ∆PQR = 1210+6+16⇒area of ∆PQR = 12×32⇒area of ∆PQR=16 square units

Example 2:If the points (–4, 1), (2, 4) and (p, 6) are collinear, then find the value of p.

Solution:

Since (–4, 1), (2, 4), (p, 6) are collinear, the area of the triangle formed by these points is zero.

∴ 12-44-6+26-1+p1-4=0⇒8+10-3p=0⇒18-3p=0⇒3p=18⇒p=183⇒p=6

Coordinate Geometry online mcq quiz started from here

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