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Question
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.
Options
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.
Solution
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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