Q.7. A point P divides the line segment joining the points A(2,-5) and B(5, 2) in the ratio 2:3. The quadrant in which point P lies is (a) Quadrant I (b) Quadrant II I AABC. DE = R^ tha AD AF (c) Quadrant III (d) Quadrant IV
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Answer:
To find the position of point P, we can use the section formula.
Let the coordinates of point P be (x, y).
According to the section formula, the x-coordinate of P is given by:
x = (3 * x-coordinate of A + 2 * x-coordinate of B)/(3+2)
= (3 * 2 + 2 * 5)/(3+2)
= (6 + 10)/5
= 16/5
Similarly, the y-coordinate of P is given by:
y = (3 * y-coordinate of A + 2 * y-coordinate of B)/(3+2)
= (3 * -5 + 2 * 2)/(3+2)
= (-15 + 4)/5
= -11/5
So, the coordinates of point P are (16/5, -11/5).
To determine the quadrant in which point P lies, we need to analyze the signs of its x and y coordinates.
Since the x-coordinate (16/5) is positive and the y-coordinate (-11/5) is negative, point P lies in Quadrant IV.
Therefore, the correct answer is (d) Quadrant IV.
Answer:
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Step-by-step explanation:
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