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प्रश्न
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
विकल्प
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
उत्तर
Assertion (A) is true, but Reason (R) is false.
Explanation:
The coordinates of the point that divides a line segment with endpoints (x1, y1) and (x2, y2) in the ratio m:n are given by the section formula:
`((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))`
Here, if the point (−3, k) divides the segment in the ratio 1: 2 between (−5, 4) and (−2, 3), then we can plug these values into the section formula:
`- 3 = (1(-2) + 2(-5))/(1 + 2)`
`- 3 = (- 2 - 10)/3`
`-3 = -4`
This is not true. Therefore, the x - x-coordinate does not satisfy the 1:2 division ratio.
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