# Worksheet on Two-point Form

Practice the questions given in the worksheet on two-point form of the straight line.

If a straight line passes through the points (x(_{1}\), y(_{1}\)) and (x(_{2}\), y(_{2}\)) then its equation is y - y$$_{1}$$ = $$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$$(x - x$$_{1}$$), and the slope of the straight line is $$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$$

1. Find the equations of the straight lines joining each of the following pair of points

(i) (- 3, - 4) and (2, 5)

(ii) (0, b) and (- a, 0)

(iii) (at$$_{1}$$$$^{2}$$, 2at$$_{1}$$) and (at$$_{2}$$$$^{2}$$, 2at$$_{2}$$)

(iv) (a cos α, a sin α) and (a cos β, a sin β).

2. Find the equation and the slope of the line joining the points

(i) (1, 6), (6, 1)

(ii) (-2, 1), (3, -2)

(iii) Origin and (-3, 1)

(iv) (3, 4), (-2, 4)

(v) (7, 0), (0, 3)

3. Find the equation and the slope of the line joining the points A on the x-axis and B on the y-axis if

(i) OA = 4, OB = 5

(ii) OA = -2, OB= 3

(iii) OA = -1, OB = -2, where O is the origin.

Answers for the worksheet on two-point form of the straight line are given below:

1. (i) 9x  - 5y + 7 = 0

(ii) bx - ay + ab = 0

(iii) y(t$$_{1}$$ +  t$$_{2}$$) - 2x =  2at$$_{1}$$t$$_{2}$$

(iv) x cos$$\frac{α + β}{2}$$ +  y sin$$\frac{α + β}{2}$$ =  a cos$$\frac{α - β}{2}$$

2. (i) x + y - 7 = 0

(ii) 3x + 5y + 1 = 0

(iii) x + 3y = 0

(iv) y = 4

(v) 3x + 7y - 21 = 0

3. (i) 5x + 4y - 20 = 0

(ii) 3x - 2y + 6 = 0

(iii) 2x + y + 2 = 0

Equation of a Straight Line