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Question
The co-ordinates of two points A and B are (–3, 4) and (2, –1). Find:
- the equation of AB;
- the co-ordinates of the point where the line AB intersects the y-axis.
Solution
i. Given, co-ordinates of two points A and B are (–3, 4) and (2, –1).
Slope = `(-1 - 4)/(2 + 3) = (-5)/5 = -1`
The equation of the line AB is given by:
y − y1 = m(x − x1)
y + 1 = −1(x − 2)
y + 1 = −x + 2
x + y = 1
ii. Let the line AB intersects the y-axis at point (0, y).
Putting x = 0 in the equation of the line, we get,
0 + y = 1
y = 1
Thus, the co-ordinates of the point where the line AB intersects the y-axis are (0, 1).
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