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If the mid – point of the line segment joining the points (a, b – 2) and ( – 2, 4) is (2, – 3), then the values of ‘a’ and ‘b’ are
- a)6, 8
- b)4, – 5
- c)6, – 8
- d)– 6, 8
Correct answer is option 'C'. Can you explain this answer?
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If the mid – point of the line segment joining the points (a, b ...
Explanation:
Let the coordinates of midpoint O(2,−3) is equidistance from the points A(a,b−2) and B(−2,4).
Most Upvoted Answer
If the mid – point of the line segment joining the points (a, b ...
To find the values of a and b, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by the average of their x-coordinates and the average of their y-coordinates.
Midpoint formula:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
Given that the midpoint of the line segment joining the points (a, b 2) and (2, 4) is (2, 3), we can set up the following equation:
(2, 3) = ((a + 2)/2, (b + 4)/2)
Simplifying the equation, we have:
2 = (a + 2)/2
3 = (b + 4)/2
To solve for a, we can cross-multiply:
4 = a + 2
Subtracting 2 from both sides, we get:
2 = a
Therefore, the value of a is 2.
To solve for b, we can again cross-multiply:
6 = b + 4
Subtracting 4 from both sides, we get:
2 = b
Therefore, the value of b is 2.
Hence, the values of a and b are both equal to 2.
Thus, the correct answer is option C: 6, 8.
Midpoint formula:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
Given that the midpoint of the line segment joining the points (a, b 2) and (2, 4) is (2, 3), we can set up the following equation:
(2, 3) = ((a + 2)/2, (b + 4)/2)
Simplifying the equation, we have:
2 = (a + 2)/2
3 = (b + 4)/2
To solve for a, we can cross-multiply:
4 = a + 2
Subtracting 2 from both sides, we get:
2 = a
Therefore, the value of a is 2.
To solve for b, we can again cross-multiply:
6 = b + 4
Subtracting 4 from both sides, we get:
2 = b
Therefore, the value of b is 2.
Hence, the values of a and b are both equal to 2.
Thus, the correct answer is option C: 6, 8.
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