Question 11
Question: The vertices of a triangle are (0,0), (a, b) and (b, -a), find the equation to the sides of the triangle.
Answer: Let O (0,0), A (a, b) and B (b, -a) be the vertices of the triangle OAB.
ay = bx or bx - ay = 0
Equation of side OB is
by = -ax
ax + by = 0
Equation of the side AB is
Question 12
Question: Find the equation of the line through A (3,0) and B (0, -3).
Answer: Let P (x, y) be any point on the line joining A and B.
\ Equation of line is
Question 13
Question: Reduce each of the following straight line equation to the slope-intercept form. Find m and c.
Answer: The slope-intercept form of the equation of line is y = mx + c.
Question 14
Question: Find the equation of the line through (1,2) and parallel to x + 3y = 1.
Answer: Given line is x + 3y = 1.
The line passes through (1,2).
Let P (x, y) be any point on the required line.
Aliter:
The line parallel to x + 3y - 1 = 0 is x + 3y = k.
This line passes through (1,2).
Putting x = 1 and y = 2 in x + 3y = k, we have
The equation of the required line is x + 3y = 7.
Question 15
Question: Find the equation of the line with y-intercept 7 and parallel to
4x + 5y = 8.
Answer: Reduce the equation to y = mx + c form .
But c = 7,
Question 16
Question: Find the value of 'a' for which the lines ax + 4y + 5 = 0 and 9x + ay - 4 = 0 are parallel to each other.
Answer: ax + 4y + 5 = 0 and 9x + ay - 4 = 0 are parallel to each other, the slopes are equal.
Question 17
Question: Find the equation of the line perpendicular to the line 8x + 5y = 7 and passing through (1, 2).
Answer: 
(
Product of slopes of two perpendicular lines = -1)
Aliter:
Given line is 8x + 5y = 7.
The line perpendicular to 8x + 5y = 7 is 5x - 8y = k.
This line passes through (1,2).
The required equation of the line is
5x - 8y = -11 or 5x - 8y + 11 = 0
Question 18
Question: Find the equation of the line, which bisects the line joining (3, -1) and (5,11) and also bisects the distance between the points (-5,2) and (9,6).
Answer: The co-ordinates of the middle point of the line joining (3,-1) and (5,11) is
Let P (4,5) be the point.
The co-ordinates of the middle point of the line joining (-5,2) and (9, 6) is
Let Q (2,4) be the point.
We have to find the equation of the line joining the points P and Q.
Question 19
Question: 
Answer: 
\ The required equation is
Question 20
Question: Find the image of the point (-1,1) w.r.t to the line 3x + 4y = 32.
Answer: 
Let the image of the point P (-1,1) about the line AB be Q (h,k).
PQ is perpendicular to AB and is bisected at C.
Solving (ii) and (i) for h and k, we have
Reflection of P (-1,1) about the line 3x + 4y = 32 is
