Class 10

Math

All topics

Coordinate Geometry

In Fig. 3, the area of triangle ABC (in sq. units) is :

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If $(1,4)$ is the centroid of a triangle and the coordinates of its any two vertices are $(4,−8)$ and $(−9,7),$ find the area of the triangle.

Find the length of altitude through $A$ of the triangle $ABC,$ where $A≡(−3,0)B≡(4,−1),C≡(5,2)$

If $A(x_{1},y_{1}),B(x_{2},y_{2}),$ and $C(x_{3},y_{3})$ are three non-collinear points such that $x12+y12=x22+y22=x32+y32,$ then prove that $x_{1}sin2A+x_{2}sin2B+x_{3}sin2C=y_{1}sin2A+y_{2}sin2B+y_{3}sin2C=0.$

If $x_{1},x_{2},x_{3}$ as well as $y_{1},y_{2},y_{3}$ are in $GP$ with the same common ratio, then the points $(x_{1},y_{1}),(x_{2},y_{2}),$ and $(x_{3},y_{3})˙$ lie on a straight line lie on an ellipse lie on a circle (d) are the vertices of a triangle.

Prove that the circumcenter, orthocentre, incenter, and centroid of the triangle formed by the points $A(−1,11),B(−9,−8),$ and $C(15,−2)$ are collinear, without actually finding any of them.

Find the coordinates of the point which divides the line segments joining the points $(6,3)$ and $(−4,5)$ in the ratio $3:2$ (i) internally and (ii) externally.

$AB$ is a variable line sliding between the coordinate axes in such a way that $A$ lies on the x-axis and $B$ lies on the y-axis. If $P$ is a variable point on $AB$ such that $PA=b,Pb=a$ , and $AB=a+b,$ find the equation of the locus of $P˙$

If line $3x−ay−1=0$ is parallel to the line $(a+2)x−y+3=0$ then find the value of $a˙$