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प्रश्न
The co-ordinates of two points P and Q are (2, 6) and (−3, 5) respectively. Find:
- the gradient of PQ;
- the equation of PQ;
- the co-ordinates of the point where PQ intersects the x-axis.
उत्तर
Given, co-ordinates of two points P and Q are (2, 6) and (–3, 5) respectively.
i. Gradient of PQ = `(5 - 6)/(-3 - 2) = (-1)/(-5) = 1/5`
ii. The equation of the line PQ is given by:
y − y1 = m(x − x1)
`y - 6 = 1/5(x - 2)`
5y − 30 = x − 2
5y = x + 28
iii. Let the line PQ intersects the x-axis at point A(x, 0).
Putting y = 0 in the equation of the line PQ, we get,
0 = x + 28
x = −28
Thus, the co-ordinates of the point where PQ intersects the x-axis are A(−28, 0).
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