Coordinate Geometry MCQs with Detailed Solutions – Level 1

Coordinate Geometry MCQs Level 1: Distance, Section Formula and Slopes

This Level 1 set contains basic coordinate geometry MCQs on the distance formula, section and midpoint formulas, centroid, area of a triangle, slopes, intercepts, collinearity and reflections. It suits school students and competitive exam aspirants revising the fundamentals. Aptitude360 gives a step-by-step worked solution for every question.

Topics covered in these coordinate geometry questions

• Distance between two points, including word problems set on maps
• Internal division of a segment and the midpoint of a line segment
• Centroid of a triangle and finding a missing vertex from the centroid
• Area of a triangle from its vertices and the triangle formed by a line with the axes
• Slope, intercepts and equations of lines, including parallel and perpendicular lines
• Collinearity of three points and reflection in the axes and the origin

Key coordinate geometry formulas for Level 1

• Distance: \( d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \)
• Section formula, ratio m : n: \( x=\dfrac{mx_{2}+nx_{1}}{m+n} \)
• Centroid x-coordinate: \( \dfrac{x_{1}+x_{2}+x_{3}}{3} \)
• Slope, with \( x_{2}\neq x_{1} \): \( m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} \)
• Perpendicular non-vertical lines: \( m_{1}\times m_{2}=-1 \)
• Triangle cut off by a line with intercepts a and b: \( \dfrac{1}{2}|ab| \)

Revision tips for basic coordinate geometry

• Rewrite a line in slope-intercept form before reading its slope
• Check collinearity by setting the triangle area formula equal to zero
• For a line meeting both axes, find the intercepts first; the triangle area is half the absolute value of their product
• Reflection in the x-axis changes only the sign of y, and reflection in the origin changes both signs

Who should practise this set

School students and aspirants starting the geometry part of quantitative aptitude who want to master the core formulas before harder levels.