Class 10  >  International Mathematics Olympiad (IMO) for Class 10  >  Math Olympiad Test: Co-ordinate Geometry- 1 Download as PDF

Math Olympiad Test: Co-ordinate Geometry- 1


Test Description

10 Questions MCQ Test International Mathematics Olympiad (IMO) for Class 10 | Math Olympiad Test: Co-ordinate Geometry- 1

Math Olympiad Test: Co-ordinate Geometry- 1 for Class 10 2022 is part of International Mathematics Olympiad (IMO) for Class 10 preparation. The Math Olympiad Test: Co-ordinate Geometry- 1 questions and answers have been prepared according to the Class 10 exam syllabus.The Math Olympiad Test: Co-ordinate Geometry- 1 MCQs are made for Class 10 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math Olympiad Test: Co-ordinate Geometry- 1 below.
Solutions of Math Olympiad Test: Co-ordinate Geometry- 1 questions in English are available as part of our International Mathematics Olympiad (IMO) for Class 10 for Class 10 & Math Olympiad Test: Co-ordinate Geometry- 1 solutions in Hindi for International Mathematics Olympiad (IMO) for Class 10 course. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free. Attempt Math Olympiad Test: Co-ordinate Geometry- 1 | 10 questions in 10 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study International Mathematics Olympiad (IMO) for Class 10 for Class 10 Exam | Download free PDF with solutions
1 Crore+ students have signed up on EduRev. Have you?
Math Olympiad Test: Co-ordinate Geometry- 1 - Question 1

Find the value of k for which the points A (3, 2), B (4, k) and C (5, 3) are collinear.

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 1

The points A (3, 2), B (4, K), and C (5, 3) are collinear then area (ΔABC) = 0
⇒ 1/2 [3(k − 3)+ 4(3 − 2) + 5(2 − k)] = 0
⇒ 3k - 9 + 4 + 10 - 5k = 0
⇒ -2k + 5 = 0 ⇒ k = 5/2

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 2

Find ratio in which the line 2x + y - 4 = 0 divides the line segment joining A(2, -2) and B(3, 7).

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 2


Let the point P (x, y) divide the line AB in the ratio k : 1

This point P(x, y) lies on the line
2x + y - 4 = 0

⇒ 6k + 4+ 7k - 2 - 4k - 4 = 0
⇒ 9k - 2 = 0 ⇒ 9k = 2
⇒ k = 2/9 = 2 : 9

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 3

The co-ordinates of ends of a diameter of a circle are (4, -1) and (-2, -5). Find the centre of the circle.

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 3

Ends of diameter of circle are (4, -1) and (-2, -5)
centre = Mid-point of (4, -1) and (-2, -5)

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 4

The area of a triangle with vertices (a, b + c) and (b, c + a) and (c, b + a) is

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 4

Area of triangle
= 1/2 [a(c + a - a - b) + b (a + b - b - c) + c (b + c - c - a)]
= 1/2 [a(c − b)+ b(a − c) + c(b − a)]
= 1/2 [ac − ab + ab − bc + bc − ac]
= 1/2 × 0 = 0

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 5

Find the co-ordinates of the points which trisects the line joining (-3, 5) and (6, -7).

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 5

Let P(x, y) be the point

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 6

The ends of a diagonal of a square have the coordinates (a, 1) and (-1, a), find a if the area of the square is 50 square units.

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 6


Let side of the square be x.
x2 + x2 = (-1 - a)2 + (a - 1)2
⇒ 2x2 = 1 + a2 + 2a + a2 + 1 - 2a
⇒ x2 = a2 + 1
⇒ 50 = a2 + 1 ⇒ a2 = 49
⇒ a = ±7

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 7

Two vertices of a triangle are (2, -4) and (1, 3). If the origin is the centroid of the triangle then what is the third vertex?

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 7


third vertex = (-3, 1)

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 8

What is the locus of a point equidistant from the point (2, 4) and y-axis?

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 8


Let, the point be P(x, y).
Given AP = BP
⇒ AP2 = BP2
⇒ (x - 2)2 + (y - 4)2 = (x - 0)2 + (y - y)2
⇒ x2 + 4 - 4x + y2 + 16 - 8y = x2
⇒ y2 - 4x - 8y + 20 = 0

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 9

If the coordinates of the mid-point of the sides of a triangle are (1, 1) (2, -3), and (3, 4) what is the centroid?

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 9



⇒ x1 + x2 = 6
y1 + y2 = 8
x2 + x3 = 2
y2 + y3 = 2
x1 + x3 = 4
y1 + y3 = -6
x1 + x2 + x3 = 12/2 = 6
x1 = 6 - 2 = 4; x2 = 2, x3 = 0
y1 + y2 + y3 = 2
y1 = 0; y2 = 8; y3 = -6
Centroid

Math Olympiad Test: Co-ordinate Geometry- 1 - Question 10

What is the value of k, so that the points A(8, 1), B(3, -4), and C(2, K) are collinear?

Detailed Solution for Math Olympiad Test: Co-ordinate Geometry- 1 - Question 10

Given points are A(8, 1), B(3, −4) and C(2, k)
It is also said that they are collinear and hence the area enclosed by them should be 0
Area of the triangle having vertices (x1, y1), (x2, y2) and (x3, y3
= 1/2 |x1(y- y3) + x2(y- y1) + x3(y- y2)| 
Given that area of ∆ABC = 0 
∴ 0 = 1/2 |8(-4 – k) + 3(k – 1) + 2(1 – (-4))| 
∴ 0 = 1/2 |-32 – 8k + 3k - 3 + 10| 
∴ 5k + 25 = 0 
∴ k = -5 
Hence, the value of k is -5.

Use Code STAYHOME200 and get INR 200 additional OFF
Use Coupon Code
Information about Math Olympiad Test: Co-ordinate Geometry- 1 Page
In this test you can find the Exam questions for Math Olympiad Test: Co-ordinate Geometry- 1 solved & explained in the simplest way possible. Besides giving Questions and answers for Math Olympiad Test: Co-ordinate Geometry- 1, EduRev gives you an ample number of Online tests for practice