Question

Q.11] Three girls Rani, Mansi and Sneha are talking to each other and
maintaining a social distance due to COVID-19. They are standing
at the vertices of a triangle, whose vertices are given in the figure.
Rani (2,-2)
Mansi (1,1)
Sneha (-1,0)
Based on the above information, answer the following:
()
The equation of the line formed by Rani and Mansi is
a) 3x-y =4 b) 3x +y =4 c)x-3y = 4 d)x +3y =4
(1)
(i) Slope of the line formed by Rani and Sneha is
b)-3/2
a) 2/3
C)-2/3
d) 1/3
(1)
(ii) The equation of altitude through Mansi is
b) 2x+3y =5
a) 3x-2y = 1
(1)
d) None of these
o)x+ 2y =3
(iv) The equation of median from Rani is
a) 5x+ 4y 2
b) 5x 4y = 2
(1)
c) 4x- 5y = 1
d) None of these
v) The equation of line passing through Rani and parallel to the
line formed by Mansi and Sneha is
a) x-2y =4
b) x+2y =6​

Answer 1

4x-d +sc+48-80=answer

Answer 2

Question (i) :- The equation of the line formed by Rani and Mansi is

a) 3x-y =4 b) 3x +y =4 c)x-3y = 4 d)x +3y =4

Solution :-

given that,

• Rani (2,-2)
• Mansi (1,1)

so,

→ slope of line = (y2 - y1)/(x2 - x1) = 1 -(-2) / (1 - 2) = (1 + 2)/(-1) = (-3) .

then,

→ Equation of line = (y - y1) = m(x - x1) => y - (-2) = (-3)(x - 2) => y + 2 = -3x + 6 => y + 3x = 6 - 2 => 3x + y = 4 (b) (Ans.)

Question (i) :- Slope of the line formed by Rani and Sneha is :- a)-3/2 b) 2/3 c)-2/3 d) 1/3

Solution :-

given that,

• Rani (2,-2)
• Sneha (-1,0)

so,

→ slope of line = (y2 - y1)/(x2 - x1) => 0 -(-2) / (-1 - 2) => 2/(-3) = (-2/3) (c) (Ans.)

Question (iii) :- The equation of altitude through Mansi is :-

a) 2x+3y =5 b) 3x-2y = 1 c) None of these d)x+ 2y =3

Solution :-

given that,

• Mansi (1,1)
• Rani (2,-2)
• Sneha (-1,0)

so,

→ Slope of Rani and sneha = (-2/3) (solved in Question 2).

then,

→ Equation of altitude passing through mansi(1,1) vertex = y - y1 = m(x - x1) => y - 1 = (-2/3)(x - 1) => 3y - 3 = -2x + 2 => 3y + 2x = 2 + 3 => 2x + 3y = 5 (a) (Ans.)

Question (iv) :- The equation of median from Rani is :-

a) 5x+ 4y = 2 b) 5x 4y = 2 c) 4x- 5y = 1 d) None of these

Solution :-

given that,

• Mansi (1,1)
• Rani (2,-2)
• Sneha (-1,0)

since the median from Rani passes through midpoint of line passing through Mansi and Sneha .

→ Midpoint of Mansi and Sneha = (x1 + x2)/2 , (y1 + y2)/2 = (1 - 1)/2 = 0 and (0 + 1)/2 = (1/2) .

then,

→ Slope of midpoint(0,1/2) and Rani coordinates(2,-2) = (y2 - y1)/(x2 - x1) => (-2 - 1/2) / (2 - 0) => (-5/2) / 2 = (-5/4) .

therefore,

→ Equation of line = y - y1 = m(x - x1) => y - (-2) = (-5/4)(x - 2) => 4y + 8 = -5x + 10 => 5x + 4y = 2 (a) (Ans.)

Question (v) :- The equation of line passing through Rani and parallel to the line formed by Mansi and Sneha is :-

a) x-2y =4 b) x+2y = 6 c) x-2y = 6 d) 2x+y = 4

Solution :-

given that,

• Mansi (1,1)
• Rani (2,-2)
• Sneha (-1,0)

→ Slope of line formed by Mansi and Sneha = (y2 - y1)/(x2 - x1) => (0 - 1) / (-1 - 1) => (-1)/(-2) = (1/2) .

now, we know that, when lines are parallel their slope is equal .

then,

→ Slope of parallel line = (1/2) .

therefore,

→ Equation of line parallel and passing through Rani = y - y1 = m(x - x1) => y - (-2) = (1/2)(x - 2) => 2y + 4 = x - 2 => x - 2y = 6 (c) (Ans.)

Learn more :-

The orthocentre of the triangle with vertices A (1 , 3), B(2 , -1) and C ( 0 , -3)

https://brainly.in/question/35183021