class 11

Math

Co-ordinate Geometry

Coordinate Geometry

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

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Find the ratio in which the point $P(43 ,125 )$ divides the line segment joining the points $A(21 ,53 )$ and $B(2,−5)$.

Show that the following points are collinear.$A(−5,1),B(5,5)$ and $C(10,7)$.

Find the area of the quadrilateral whose vertices, taken in order, are $(−4,-2), (−3,-5), (3,-2) and (2,3)˙$

Find the distance between the points:$P(asinα,acosα)$ and $Q(acosα,−asinα)$.

A train travels at a certain average speed for a distance of 54 km and then travels a distanceof 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours tocomplete the total journey, what is its first speed?

The line segment joining $A(−2,9)$ and $B(6,3)$ is a diameter of a circle with centre C. Find the coordinates of C.

Find the centre of a circle passing through the points $(6,−6),(3,−7)$ and $(3,3)$.

If the vertices of $Δ$ABC be $A(1,−3),B(4,p)$ and $C(−9,7)$ and its area is $15$ square units, find the values of p.