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:
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
● Equation of a Straight Line
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