1 Find graphically the coordinates of the vertices of a triangle whose sides have the equations: (i) y = - Maths - Pair of Linear Equations in Two Variables

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

Priyanka Kedia · Accepted Answer

$(1) T h e g i v e n e q u a t i o n c a n b e w r i t t e n a s, y = x (1) y = 0 (2) y = \frac{30 - 2 x}{3} (3) T a b l e o f v a l u e s f o r e q u a t i o n (3), i f x = 0, t h e n y = 10 i f x = 6, t h e n y = \frac{30 - 2 \times 6}{3} = 6 p l o t t h e p o int s (0, 10) a n d (6, 6) o n t h e g r a p h p a p e r, a n d c o n n e c t t h e m b y a s t r a i g h t l i n e$

$T h e l i n e s int e r \sec t a t t h e p o int A, B a n d C T h e r e f o r e, t h e v e r t i c e s o f a t r i a n g l e A B C a r e A (6, 6), B (0, 0) a n d C (15, 0)$ $(2) T h e g i v e n e q u a t i o n c a n b e w r i t t e n a s, y = x (1) y = \frac{x}{3} (2) y = 8 - x (3) T a b l e o f v a l u e s f o r e q u a t i o n (2), i f x = 3, y = 1 i f x = 6, y = 2 p l o t t h e p o int s (3, 1) a n d (6, 2) o n t h e g r a p h p a p e r, a n d c o n n e c t t h e m b y a s t r a T a b l e o f v a l u e s f o r e q u a t i o n (3), i f x = 8, t h e n y = 0 i f x = 4, t h e n y = 8 - 4 = 4 p l o t t h e p o int s (8, 0) a n d (4, 4) o n t h e g r a p h p a p e r, a n d c o n n e c t t h e m b y a s t r a i g h t l i n e$

$T h e l i n e s int e r \sec t a t t h e p o int A, B a n d C T h e r e f o r e, t h e v e r t i c e s o f a t r i a n g l e A B C a r e A (4, 4), B (0, 0) a n d C (6, 2)$ $(3) T h e g i v e n e q u a t i o n c a n b e w r i t t e n a s, y = \frac{8 + x}{2} (1) y = \frac{x + 14}{5} (2) y = 2 x + 1 (3) p l o t t h e g r a p h, w e h a v e$

$T h e l i n e s int e r \sec t a t t h e p o int A, B a n d C T h e r e f o r e, t h e v e r t i c e s o f a t r i a n g l e A B C a r e A (2, 3), B (3, 2) a n d C (1, 3)$

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

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