Question

1. Find graphically the coordinates of the vertices of a triangle whose sides have the equations:

(i) y = x, y = 0 and 2x + 3y = 30

(ii) y = x, 3y = x and x + y = 8

(iii) 2y –x = 8, 5y – x = 14 and y – 2x = 1

Answer 1

Given : Equation of sides of triangle (i) y = x, y = 0 and 2x + 3y = 30  , (ii) y = x, 3y = x and x + y = 8 (iii) 2y –x = 8, 5y – x = 14 and y – 2x = 1

To find : coordinates of the vertices of a triangle

Solution:

(i) y = x, y = 0 and 2x + 3y = 30

y  = x   and y  = 0

=> y = 0   ,  x = 0

(0,0)

y  = 0   and 2x + 3y = 30

=> 2x = 30

=> x = 15

( 15 , 0)

y = x   and 2x + 3y = 30

=> 5x = 30

=> x = 6 , y = 6

=> (6 , 6)

Vertices of triangle = (0,0) , (6 , 6)  , ( 15 , 0)

(ii) y = x, 3y = x and x + y = 8

y = x, 3y = x     => x  = 0  , y  = 0  (0,0)

y = x and x + y = 8  =>  x = 4 , y = 4  ( 4 , 4)

3y = x and x + y = 8   => x = 6 , y = 2  ( 6 , 2)

Vertices of triangle =   (0,0) ,  ( 4 , 4)  ( 6 , 2)

(iii)  2y –x = 8, 5y – x = 14 and y – 2x = 1

=>  2y –x = 8, 5y – x = 14  => x = - 4 , y = 2   (-4, 2)

2y –x = 8  and y – 2x = 1  => x = 2  , y  = 5   ( 2 , 5)

5y – x = 14 and y – 2x = 1  => x = 1   , y = 3   ( 1 , 3)

Vertices of triangle =    (-4, 2)  , ( 2 , 5) , ( 1 , 3)

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Answer 2

Answer:

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