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Coordinate Geometry

Short Answer Type

381.
Find the distance of a point P(x, y) from the origin.

Given point is P(x,y)

Origin point is O (0,0)

Using distance formula

$P O = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(x - 0)^{2} + (y - 0)^{2}} = \sqrt{x^{2} + y^{2}}$

382.

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

383.

Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division

Long Answer Type

384.

Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right
triangle

385.

If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that x + y = 15.

Multiple Choice Questions

386.

In fig., the area of triangle ABC (in sq. units) is

Long Answer Type

387.

Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division

388.

Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

389.

A(4, - 6), B(3,- 2) and C(5, 2) are the vertices of a ΔABC and AD is its median. Prove that the median AD divides ΔABC into two triangles of equal areas.