15+ CAT Coordinate Geometry Questions PDF With Video Solutions

Co-ordinate Geometry questions in CAT essentially tests the concepts of Geometry and Algebra. We have compiled a List of Top 15 Co-ordinate Geometry Questions for Practice with Video Solutions. Each question has a detailed video and text explanation. You could check the CAT Previous Papers for more practice and knowing the type of questions being asked in the exam. About 1-2 questions are asked each year and taking CAT mock tests regularly will familiarize you with the exam pattern and boost your confidence. Keep practicing and stay consistent!

CAT Co-ordinate Geometry Question Weightage Over Past 5 Years

Over the past years, questions from Co-ordinate Geometry weren't being asked from CAT exam syllabus. Understanding the weightage of these topics will help you prioritize where to focus. And for those seeking to understand concepts of Co-ordinate Geometry getting yourself enrolled in CAT online coaching is recommended where you get to learn time saving approaches.

CAT Co-ordinate Geometry Formulas PDF

1. Coordinate Geometry - Straight Lines

Coordinate geometry formulae:

The distance between two points with coordinates $$(x_1, y_1), (x_2, y_2)$$ is given by $$ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

Mid point between two points $$A\left(x_1,y_1\right)$$ and $$B\left(x_2,y_2\right)$$ is $$\left(\frac{\left(x_1+x_2\right)}{2},\frac{\left(y_1+y_2\right)}{2}\right)$$

Coordinates of a point P that divides the line joining $$A\left(x_1,y_1\right)$$ and $$B\left(x_2,y_2\right)$$ internally in the ratio l:m : $$\left(\frac{\left(lx_2+mx_1\right)}{l+m},\frac{\left(ly_2+my_1\right)}{l+m}\right)$$.

Coordinates of a point P that divides the line joining $$A\left(x_1,y_1\right)$$ and $$B\left(x_2,y_2\right)$$ externally in the ratio l:m : $$\left(\frac{\left(lx_2-mx_1\right)}{l-m},\frac{\left(ly_2-my_1\right)}{l-m}\right)$$.

A line can be defined as $$y=mx+c$$ where m is the slope of the line and c is the y-intercept.

Slope $$m=\frac{\left(y_2-y_1\right)}{x_2-x_1}$$. Here, if $$x_2=x_1$$, then the two lines are perpendicular to each other.

When two lines are parallel, their slopes are equal i.e $$m_1=m_2$$

When two lines are perpendicular, product of their slopes = -1 i.e $$m_1*m_2=-1$$

If a and b are the x and y intercept of a line then $$\frac{x}{a}+\frac{y}{b}=1$$

If two intersecting lines have slopes $$m_1$$ and $$m_2$$, then the angle between the two lines will be $$\tan\theta\ =\frac{\left(m_1-m_2\right)}{1+m_1m_2}$$.

The length of perpendicular from a point $$\left(X_1,Y_1\right)$$ on the line AX+BY+C=0 is $$\frac{\left(AX_1+BY_1+C\right)}{\sqrt{\ A^2+B^2}}$$.

The distance between two parallel lines Ax+By+C1 = 0 and Ax+By+C2= 0 is $$\left|\frac{C_1-C_2}{\sqrt{\ A^2+B^2}}\right|$$

Image of the point (m,n) in the line ax + by + c = 0 is given by $$\dfrac{\left(x-m\right)}{a}=\dfrac{\left(y-n\right)}{b}=-\dfrac{2\left(am+bn+c\right)}{a^2+b^2}$$