Practice the questions given in the worksheet on twopoint 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 xaxis and B on the yaxis 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 twopoint form of the straight line are given below:
Answers:
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
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