## Section Formula Worksheet Solution2

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)

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