MAH MCA CET 2024
The points , and are
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option D — Collinear
Detailed Solution
By the section formula, divides the segment from to internally in the ratio .
A point that divides a segment lies on that segment, so all three points lie on one straight line: they are collinear.
✓ Check
Take , , , : the third point is and the triangle area is .⚠ Common trap
The midpoint case makes the third point equidistant from the first two, which may suggest an isosceles triangle, option (B); but the three points are still on one line, so no triangle exists.Quick tip
Section formula: the third point divides the join of the first two in the ratio
💬 Discussions on this question
Ask a doubt ›Still stuck on this question? Ask our faculty and fellow students — answers appear here.
Ask a doubtMore Rectangular Cartesian System Questions
View all ›- Q1.A triangle has a vertex at (1, 2) and the midpoints of the two sides through it are (−1, 1) and (2, 3). Then the area of this triangle is
- Q2.The perpendicular distance of the point from the line is
- Q3.The projections of a line segment on the axes are respectively. The length and direction cosines are
- Q4.The two lines and intersect at the point lies on the curve whose equation is
- Q5.If , , are the vertices of a , then as varies, the locus of its centroid is,
More Quantitative Aptitude Questions
- Q1.By selling 45 lemons for ₹40, a man loses 20%. How many lemons should he sell for ₹24 to gain 20%?Profit, Loss & Discount
- Q2.The marked price of an article is 1.45 times its cost price. Its selling price is ₹1,500 and the profit is 25%. What is the discount percentage? Profit, Loss & Discount
- Q3.Let A be a real number. Then the roots of the equation are real and distinct if and only if Quadratic Equations
- Q4.The number of distinct real roots of the equation is Quadratic Equations
- Q5.The roots of are:Quadratic Equations
Rectangular Cartesian System — Preparation
This question tests your understanding of Rectangular Cartesian System, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
The rectangular Cartesian coordinate system locates any point in a plane by its distances from two perpendicular axes, written as an ordered pair (x, y). It is the starting point for all of coordinate geometry. This topic covers quadrants, the distance formula, the section formula (internal and external division), the midpoint formula, the area of a triangle from its vertices, and collinearity of points. It also covers special points of a triangle such as the centroid, incentre and circumcentre, and the locus of a point. A useful check is that three points are collinear exactly when the area of the triangle they form is zero. Questions here are usually formula-based and can be solved quickly with careful sign handling. Practise the Cartesian coordinate system questions below, each with a step-by-step solution.