Is Three Dimensional Coordinates part of the EAPCET Mathematics syllabus?

Yes. Three Dimensional Coordinates is taught in Intermediate first year · Paper IB Mathematics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.

How many Mathematics questions are there in EAPCET?

80 of the 160 questions in the Engineering paper are Mathematics, spread across 37 chapters.

What mistakes do students make in Three Dimensional Coordinates?

Pairing m with the first point in the section formula; for the ratio m : n, m multiplies the coordinates of the second point. Setting z = 0 for the YZ-plane; the YZ-plane is the plane x = 0. Dividing by 3 for the centroid of a tetrahedron; it has four vertices, so divide their sum by 4. Declaring points collinear because two distances are equal; check that the two shorter distances add up to the longest one.

EAPCET Mathematics · Intermediate first year · Paper IB

Three Dimensional Coordinates

Three Dimensional Coordinates extends distance and section formulas to space. It is short and mechanical, which makes it reliable scoring.

Subject: Mathematics
Taught in: Intermediate first year · Paper IB
Mathematics in the paper: 80 of 160 questions

Key formulas and results

Distance $= \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}}$
Section formula: $\left(\dfrac{mx_{2} + nx_{1}}{m + n}, \dfrac{my_{2} + ny_{1}}{m + n}, \dfrac{mz_{2} + nz_{1}}{m + n}\right)$
Centroid of a triangle: average of the three vertices
Centroid of a tetrahedron: average of the four vertices

What this chapter covers

Coordinates in space
Distance formula
Section formula
Centroid of a triangle and tetrahedron

How it is usually asked

Find a distance or test collinearity
Find the ratio in which a plane divides a segment
Find a centroid

Understanding Three Dimensional Coordinates

Three mutually perpendicular axes through an origin locate every point in space by an ordered triple (x, y, z). The three coordinate planes, the XY, YZ and ZX planes, divide space into eight octants, and the signs of the coordinates tell you which octant a point is in. On the XY-plane z = 0, on the YZ-plane x = 0 and on the ZX-plane y = 0.

The plane formulas extend naturally. The distance between two points is √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²], and the point dividing a segment in the ratio m : n uses the section formula in each coordinate. The centroid of a triangle is the average of its three vertices, and the centroid of a tetrahedron is the average of its four vertices.

EAPCET questions here are mechanical: find a distance, test whether three points are collinear, find a centroid or a missing vertex, or find the ratio in which a coordinate plane divides a segment. That last type is solved by setting the relevant coordinate of the section point to zero; a negative ratio means the division is external.

Worked example

EAPCET-style question

The ratio in which the $YZ$ -plane divides the segment joining $(4, -1, 3)$ and $(-6, 2, 5)$ is

(1)2 : 3 internally
(2)3 : 2 internally
(3)2 : 3 externally
(4)3 : 2 externally

Solution

On the $YZ$ -plane $x = 0$ . Let the ratio be $m : n$ .
The $x$ -coordinate of the dividing point is $\dfrac{m(-6) + n(4)}{m + n} = 0$ .
So $4n = 6m$ , giving $m : n = 2 : 3$ .
The ratio is positive, so the division is internal; the point is $\left(0, \tfrac{1}{5}, \tfrac{19}{5}\right)$ .

Answer: 2 : 3 internally

Common mistakes to avoid

Pairing m with the first point in the section formula; for the ratio m : n, m multiplies the coordinates of the second point.
Setting z = 0 for the YZ-plane; the YZ-plane is the plane x = 0.
Dividing by 3 for the centroid of a tetrahedron; it has four vertices, so divide their sum by 4.
Declaring points collinear because two distances are equal; check that the two shorter distances add up to the longest one.

How to prepare it

The ratio in which a coordinate plane divides a segment comes from setting that coordinate to zero in the section formula.

Once the formulas feel familiar, test them the way the exam does: practise Three Dimensional Coordinates questions chapter-wise, then attempt a full previous year paper to see whether it holds up under a 3-hour timer.

Related Mathematics chapters

See every chapter in the EAPCET Mathematics syllabus.

Practise Three Dimensional Coordinates chapter-wise

Chapter-wise quizzes show exactly which topics in this chapter you still get wrong — before a full paper does.

Frequently asked questions

Is Three Dimensional Coordinates part of the EAPCET Mathematics syllabus?: Yes. Three Dimensional Coordinates is taught in Intermediate first year · Paper IB Mathematics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.
How should I prepare Three Dimensional Coordinates for EAPCET?: The ratio in which a coordinate plane divides a segment comes from setting that coordinate to zero in the section formula.
How many Mathematics questions are there in EAPCET?: 80 of the 160 questions in the Engineering paper are Mathematics, spread across 37 chapters.
What mistakes do students make in Three Dimensional Coordinates?: Pairing m with the first point in the section formula; for the ratio m : n, m multiplies the coordinates of the second point. Setting z = 0 for the YZ-plane; the YZ-plane is the plane x = 0. Dividing by 3 for the centroid of a tetrahedron; it has four vertices, so divide their sum by 4. Declaring points collinear because two distances are equal; check that the two shorter distances add up to the longest one.