In this page section formula worksheet solution2 we are going to see solution for each questions with detailed explanation.

(4) If the centroid of the triangle is at (1 , 3) and two of its vertices are (-7,6) and (8,5) then find the third vertex of the triangle.

**Solution:**

Let A (-7 , 6) B (8 , 5) and C (a , b) are the three vertices of the triangle.

centroid of the triangle = (1 , 3)

Centroid of the triangle = (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3

(1 , 3) = (-7 + 8 + a)/3 ,(6 + 5 + b)/3

(1 , 3) = (1 + a)/3 ,(11 + b)/3

Equating x and y coordinates

(1+a)/3 = 1 (11+b)/3 = 3

1 + a = 3 11 + b = 9

a = 3 – 1 b = 9 -11

a = 2 b = -2

Therefore the missing vertex
of the triangle is (2,-2)

(5) Using the section formula,show that the points A(1,0),B (5,3),C (2,7) and D(-2,4) are vertices of a parallelogram taken in order.

**Solution**

The midpoint of the diagonals AC and the diagonal BD coincide

Section formula internally = (Lx₂+mx₁)/(L+m),(Ly₂+my₁)/(L+m)

L = 1 m = 1

The midpoint of the diagonals AC. The midpoint of diagonal is in the ration 1:1

= [(1x2) + (1x1)]/(1+1) , [(1x7) + (1x0)]/(1+1)

= (2 + 1)/2 , (7 + 0)/2

= 3/2 , 7/2 ------- (1)

The midpoint of the diagonals BD. The midpoint of diagonal is in the ration 1:1

= [(1x(-2)) + (1x5)]/(1+1) , [(1x4) + (1x3)]/(1+1)

= (-2 + 5)/2 , (4 + 3)/2

= 3/2 , 7/2 ------- (2)

Two diagonals are intersecting at the same point. So the given vertex forms a parallelogram.

(6) Find the coordinates of the point which divides the line segment joining (3, 4) and (-6,2) in the ratio 3:2 externally.

**Solution:**

Section formula externally = (Lx2 - mx1)/(L - m) , (Ly2 - my1)/(L - m)

A (3, 4) B (-6,2) 3 : 2

L = 3 m = 2

= [(3x(-6)) - (2x3)]/(3-2) , [(3x2) - (2x4)]/(3-2)

= (-18 - 6)/1 , (6 - 8)/1

= (-24 , -2)

section formula worksheet solution2 section formula worksheet solution2

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