A straight line PQ cuts the x and y axis at M and N respectively. If the points A(-3, 5) and B(4, 7) lie on PQ, calculate :
i) the gradient of PQ
ii) the equation of PQ iii ) /AB/, correct to one decimal place iii) the coordinate of M and N iv) the area of triangle OMN.
Please help me with this question. Thanks.?
2016-06-19 4:44 pm
回答 (1)
2016-06-19 5:14 pm
✔ 最佳答案
(i)The gradient of PQ
= (5 - 7) / (-3 - 4)
= 2/7
(ii)
Consider a point (x, y) on PQ.
Slope of PQ :
(y - 7)/(x - 4) = 2/7
2(x - 4) = 7(y - 7)
2x - 8 = 7y - 49
Equation of PQ :
2x - 7y + 41 = 0
(iii)
When y = 0 :
2x + 41 = 0
x = -41/2
The coordinations of M = (-41/2, 0)
When x = 0 :
-7y + 41 = 0
y = 41/7
The coordinations of N = (0, 41/7)
(iv)
The area of ΔOMN
= (1/2) × (41/2) × (41/7)
= 1681/7 (square units)
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