TRIANGLE WITH THREE VERTICES

Triangle with three vertices :

Here 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)

Solution

(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

Solution

(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)

Solution

(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)

Solution

(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

Solution

(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.

Solution

Related topics

• Section formula
• Area of quadrilateral
• Centroid
• Midpoint
  
• Distance between two points
• Distance between two points worksheet
  
• Slope of the line
• Equation of the line
• Equation of line using two points worksheet 
• Equation of the line using point and slope worksheets
• Point of intersection of two lines
• concurrency of straight line
• Circumcentre of a triangle
• Orthocentre of a triangle
• Incentre of a triangle
• Locus
• Perpendicular distance
• Angle between two straight lines
  
• Equation of a circle
• With center and radius
• With endpoints of a diameter
• Equation of a circle passing though three points
• Length of the tangent to a circle
• Equation of the tangent to a circle
• Family of circles
• Orthogonal circles

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