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Question
Find the mid-point of the line segment joining the points
(−2, 3) and (−6, −5)
Solution
Mid−point of a line = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
Mid−point of AB = `((-2 - 6)/2, (3 - 5)/2)`
= `((-8)/2, (-2)/2)`
= (−4, −1)
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RELATED QUESTIONS
In the given figure, P(4, 2) is mid-point of line segment AB. Find the co-ordinates of A and B.
P(4, 2) and Q(–1, 5) are the vertices of parallelogram PQRS and (–3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.
Complete the table below the graph with the help of the following graph.
| Sr. No. | First point | Second point | Co-ordinates of first point (x1 , y1) | Co-ordinates of second point (x2 , y2) | `(y_2 - y_2)/(x_2 - x_2)` |
| 1 | C | E | (1, 0) | (3,4) | `4/2=2` |
| 2 | A | B | (-1,-4) | (0,-2) | `2/1 = 2` |
| 3 | B | D | (0,-2) | (2,2) | `4/2=2` |
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(a+b, b-a) and (a-b, a+b)
Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex.
Find the mid-point of the line segment joining the points
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O(0, 0) is the centre of a circle whose one chord is AB, where the points A and B are (8, 6) and (10, 0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD.
If `"P"("a"/3, "b"/2)` is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is
The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is
From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.
Solution:
Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.
Using midpoint formula,
x = `(5 + 3)/2`
∴ x = `square`
y = `(-3 + 5)/2`
∴ y = `square`
Using distance formula,
∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`
∴ AD = `sqrt((square)^2 + (0)^2`
∴ AD = `sqrt(square)`
∴ The length of median AD = `square`
