Class 10

Math

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Coordinate Geometry

Point $P(5,−3)$is one of the two points of trisection of the line segment joining the points $A(7,−2)andB(1,−5)$near to $A$. Find the coordinates of the other point of trisection.

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If a vertex of a triangle is $(1,1)$ , and the middle points of two sides passing through it are $−2,3)$ and $(5,2),$ then find the centroid and the incenter of the triangle.

Find the area of the triangle formed by joining the mid–points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

The maximum area of the triangle whose sides a,b and c satisfy $0≤a≤1,1≤b≤2and2≤c≤3$ is

A straight line is drawn through $P(3,4)$ to meet the axis of $x$ and $y$ at $AandB$ , respectively. If the rectangle $OACB$ is completed, then find the locus of $C˙$

Determine $x$ so that the line passing through $(3,4)and(x,5)$ makes an angle of $135_{0}$ with the positive direction of the x-axis.

Find the locus of a point, so that the join of $(−5,1)$ and $(3,2)$ subtends a right angle at the moving point.

If the line passing through $(4,3)and(2,k)$ is parallel to the line $y=2x+3,$ then find the value of $k˙$

The coordinates of the point $AandB$ are (a,0) and $(−a,0),$ respectively. If a point $P$ moves so that $PA_{2}−PB_{2}=2k_{2},$ when $k$ is constant, then find the equation to the locus of the point $P˙$