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प्रश्न
Point P is midpoint of segment AB where A(– 4, 2) and B(6, 2), then the coordinates of P are ______
पर्याय
(–1, 2)
(1, 2)
(1, –2)
(–1, 2)
उत्तर
(1, 2)
A(x1, y1) = A( –4, 2), B(x2, y2) = B(6, 2)
Here, x1 = – 4, y1 = 2, x2 = 6, y2 = 2
∴ Co-ordinates of the midpoint of seg AB
= `((x_1 + x_2)/2, (y_1 + y_2)/2)`
= `((-4 + 6)/2, (2 + 2)/2)`
= `(2/2, 4/2)`
= (1, 2)
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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`
