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प्रश्न
The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
पर्याय
I quadrant
II quadrant
III quadrant
IV quadrant
उत्तर
The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the IV quadrant.
Explanation:
If P(x, y) divides the line segment joining A(x1, y2) and B(x2, y2) internally in the ratio m : n,
Then x = `(mx_2 + nx_1)/(m + n)` and y = `(my_2 + ny_1)/(m + n)`
Given that,
x1 = 7, y1 = – 6,
x2 = 3, y2 = 4,
m = 1 and n = 2
∴ x = `(1(3) + 2(7))/(1 + 2)`, y = `(1(4) + 2(-6))/(1 + 2)` ...[By section formula]
⇒ x = `(3 + 14)/3`, y = `(4 - 12)/3`
⇒ x = `17/3`, y = `-8/3`
So, (x, y) = `(17/3, -8/3)` lies in IV quadrant. ...[Since, in quadrant, x-coordinate is positive and y-coordinate is negative]
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Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. |
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OR
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