Coordinate Geometry Questions for CAT

What will be the reflection of the point $(4,5)$ in the second quadrant?

In the provided triangle, the areas of triangles $ABD$, $ABE$, and $ADC$ form an arithmetic progression in that order. The length $BE$ is given to be $14$ cm, and it is known that the lengths (in cm) of $DC$ and $BD$ are prime numbers, where $BD$ is greater than $5$ cm. What would be the value of $DC^2 − BD^2$?

A rectangular field has an area of 20 sq. km. If the perimeter of the field is 18 km, what is the length of the longer side of the field?

What can be said about the equation of the straight line $y = -8$?

Find the mid-point of the line segment made by joining the points (3, 2) and (6, 4).

The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

New equation of 3x + 4y = 6 if origin shifts to (3, –4):

A rhombus has vertices (2,-2) and (2,7), with one diagonal on line $x-y+5=0$. Find area of rhombus.

Length of the perpendicular from (–3, –4) to line 12(x + 6) = 5(y – 2):

A rhombus PQRS is given, such that the perimeter is 148 cm. The midpoints of two adjacent sides of the rhombus are joined by a line with a length of 12 cm. Find the area (in $cm^2$) of the rhombus.

In the rectangle WXYZ given below WZ = 13 cm, WX = 5 cm and ZV = 10 cm. a,b and c represent the measure of angle ZWV, WVZ and VZW respectively. Which of the following options accurately shows the relation between a, b and c?

A solid cylindrical wafer of height 10 cms and radius 3.5 cms is cut into two equal halves along its height. The two halves are then attached to each other along their flat surfaces such that they make a cross.(90 degree angle with each other). If the cross is then coated uniformly with 1mm layer of chocolate, what is the volume of chocolate needed? (in cm3)

A ship is moving at uniform speed towards a lighthouse. X is the time taken for the angle of elevation to change from 30 degrees to 45 degrees. Y is the time taken for it to change from 45 to 60 degrees. What is the ratio of X:Y?

Aman plotted 3 points on a sheet of graph paper. He joined them to get a triangle. He then plotted the coordinates of the circumcentre, the orthocentre and the centroid and found the distance between each point. He only remembered the x‑coordinates of the vertices: 5, 6, 7, the y‑coordinate of the centroid = 3, and the orthocentre = (−8,1). What can be said about the distance 'D' between the circumcentre and the centroid?

There are two non-overlapping circles, $C_1$ and $C_2$, with radii $r_1$ and $r_2$, with the distance between their centres $d=25$ cm and the difference in their radii $(r_2-r_1)=7$ cm. If the length of the direct common tangent between $C_1$ and $C_2$ is $l$ cm. Find the number of scalene triangles with integer lengths (in cm) that can be formed using $l$ as the perimeter.

Circle C has radius 3 units. PQ is the only diameter parallel to the x-axis. P lies on y=ax and Q on y=2ax+6, where a<1. Find the value of a.

The area of the quadrilateral bounded by the Y-axis, the line x=6, and the lines |x−y|−|x−6|=4, is

A circular area of radius 7m is marked inside a square plot of side 15m. A man starts digging this circular area such that the earth so collected is evenly spread on the remaining area. The total depth of the cylinder so formed is 4m. If he charges his work at a rate of Rs 450 per cubic meter, find the total earnings of the man?

The line 5x + 2y - 20 = 0 intersects the coordinate axes to form a triangle. Find the integer closest to the radius of its circumcircle.

In the diagram given below, ABCDE is a regular pentagon. A circle is drawn such that it touches the sides BC and DE at B and E respectively. B and E are connected to a point F which lies on the circle. What is the angle BFE?