Triangle With Three Vertices

In this page triangle with three vertices we are going to see some practice questions based on the topic area of triangle using three vertices.You can find solution for each questions of the worksheets with detailed explanation.

(1) Find the are of the triangle formed by the points.

(i) (0,0) (3,0) and (0,2)

(ii) (5,2) (3,-5) and (-5,-1)

(iii) (4,-5) (4,5) and (-1,-6)


(2) Vertices of the triangle taken in order and their areas are given below. In each of the following find the value of a.

(i) (0,0),(4,a) and (6,4) and its area is 17 sq.units

(ii) (a,a) , (4 , 5) and ( 6 , -1) and its area is 9 sq.units

(iii) (a,-3),(3,a) and (-1,5) and its area is 12 sq.units


(3) Determine if the following set of points are collinear or not.

(i)  (4,3) (1,2) and (-2,1)

(ii) (-2,-2) (-6,-2) and (-2,2)

(iii) (-3/2,3) (6,-2) and (-3,4)


(4) In each of the following, find the value of k for which the given points are collinear.

(i) (k,-1)  ( 2 ,1) and (4,5)

(ii) (2,-5)  ( 3 ,-4) and (9,k)

(iii) (k,k)  (2 ,3) and (4,-1)


(5) If the three points (h,0) (a,b) and (0,k) lie on a straight line, then using the area of the triangle formula show that (a/h) + (b/k) = 1,where h,k≠ 0


(6) Find the area of the triangle formed by joining the midpoints of the sides of a triangle whose vertices are (0,-1) (2,1) and (0,3). Find the ratio of this area to the area of the given triangle.


triangle with three vertices triangle with three vertices

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”