List of top Mathematics Questions on Coordinate Geometry asked in KEAM

Let \( ABC \) be an equilateral triangle. If the coordinates of \( A \) are \( (-2,2) \) and the side \( BC \) is along the line \( x + y = 6 \), then the length of the side of the triangle is

The area of the triangle bounded by the lines $x = 4$, $y = -4$ and $y = x$ is

The area of a triangle is 5 sq. units. Two of its vertices are (2,1) and (3,-2). The third vertex lies on \( y = x + 3 \). The coordinates of the third vertex can be

If the points \( (2a,a), (a,2a), (a,a) \) form a triangle of area 18, find centroid

The area of the triangle formed by the points \( (a,b+c), (b,c+a), (c,a+b) \) is

If \( (x,y) \) is equidistant from \( (a+b,b-a) \) and \( (a-b,a+b) \), then

The area of a triangle is 5 sq. units. Two of its vertices are (2,1) and (3,-2). The third vertex lies on \( y = x + 3 \). The coordinates of the third vertex can be

If the points \( (2a,a), (a,2a), (a,a) \) form a triangle of area 18, find centroid

The area of the triangle formed by the points \( (a,b+c), (b,c+a), (c,a+b) \) is

If \( (x,y) \) is equidistant from \( (a+b,b-a) \) and \( (a-b,a+b) \), then

The area of a triangle is 5 sq. units. Two of its vertices are (2,1) and (3,-2). The third vertex lies on \( y = x + 3 \). The coordinates of the third vertex can be

The area of the triangle formed by the points \( (a,b+c), (b,c+a), (c,a+b) \) is

If \( (x,y) \) is equidistant from \( (a+b,b-a) \) and \( (a-b,a+b) \), then

If the points \( (2a,a), (a,2a), (a,a) \) form a triangle of area 18, find centroid

The area of the parallelogram with vertices \( (0, 0), (7, 2), (5, 9) \) and \( (12, 11) \) is:

The set \( \{ (x, y) : |x| + |y| = 1 \ \) in the \( xy \) plane represents:}

Let \( A(6, -1) \), \( B(1, 3) \) and \( C(x, 8) \) be three points such that \( AB = BC \). The values of \( x \) are:

Area of the triangle with vertices \( (-2, 2), (1, 5) \) and \( (6, -1) \) is:

If \( (x, y) \) is equidistant from \( (a+b, b-a) \) and \( (a-b, a+b) \), then:

The points $(-1, 0)$ and $(-2, 1)$ are the two extremities of a diagonal of a parallelogram. If $(-6, 5)$ is the third vertex, then the fourth vertex of the parallelogram is:

If the orthocenter, centroid, incenter and circumcentre coincide in a triangle $ABC$, and if the length of side $AB$ is $\sqrt{75}$ units, then the length of the altitude of the triangle through the vertex $A$ is:

If $A(2, 4)$ and $B(6, 10)$ are two fixed points and if a point $P$ moves so that $\angle APB$ is always a right angle, then the locus of $P$ is:

The line segment joining \( (5,0) \) and \( (10\cos\theta, 10\sin\theta) \) is divided internally in the ratio \(2:3\) at \(P\). If \(\theta\) varies, then the locus of \(P\) is

Let \( A(0,0) \) and \( B(8,0) \) be two vertices of a right angled triangle whose hypotenuse is \( BC \). If the circumcentre is \( (4,2) \), then the point \( C \) is:

If coordinates of the circumcentre and the orthocentre of a triangle are respectively \( (5,5) \) and \( (2,2) \), then the coordinates of the centroid are: