Question 11
Question: Find the equation of the line through the points
Answer: Let R (x, y) be any point on the line joining the point P and Q.
\The equation of the line is
Question 12
Question: The vertices of the triangle are (0,0), (4,6) and (8,4). Find the equation of its sides.
Answer: 
Let O (0,0), A (4,6) and B (8,4) be the vertices of D OAB.
Equation of the side OA is
Equation of the side OB is
Equation of the side AB 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.
i)
Divide by the coefficient of y i.e., by 3.
Then,
Comparing with y = mx+c, we have m = 3 and c = 9.
Dividing the coefficient of y i.e., by 3, we get
Question 14
Question: Write the equation of the line passing through the origin with slope m.
Answer: Let the equation of the line be y = mx + c.
This must pass through (0,0).
\The required equation of the line is y = mx.
Question 15
Question: Find the equation of the line passing through (5,1) and parallel to 7x - 2y = 10.
Answer: The line parallel to 7x - 2y = 10 is 7x - 2y = k.
This line must pass through (5,1).
\The equation of the required line is 7x - 2y = 33.
Question 16
Question: If the lines ax + by + c = 0 and a'x + b'y + c' = 0 are parallel then show that ab' = a'b.
Answer: Reduce both line equations to slope-intercept form, then we get
ii) Intercept form
Since the lines are parallel, their slopes must be identical.
Question 17
Question: Find the equation of the perpendicular bisector of the line segment joining the points (-4,5) and (2,9).
Answer: Let P (x, y) be any point on the perpendicular bisector.
\Equation of the perpendicular bisector through (-1,7) is
Question 18
Question: Find the equation of the straight line which bisects the distance between the two points (3, -4) and (5,6) and also bisects the distance between the points (-6,3) and (-10,7).
Answer: Co-ordinates of the mid-point of the line joining (3, -4) and (2,6) is
Co-ordinates of the mid-point of the line joining (-6,3) and (-10,7)
We have to find the equation of the line joining the points P and Q.
Question 19
Question: 
Answer: 
Question 20
Question: Find the image of the point (4,3) with respect to the mirror line x + y - 5 = 0.
Answer: Let the image of the point P (4,3) be Q (h, k) in the mirror line AB, whose equation is x + y - 5 = 0 ......(1)
PQ is perpendicular to AB and is bisected at C.
Since AB and PQ are perpendicular to each other, we have
Solving for h and k from the equation (ii) and (iii), we have
h = 2 and k = 1
The image of P (4,3) is Q (2,1) w.r.t line x + y - 5 = 0.
