MCQ: Coordinate Geometry - 2 - SSC CGL MCQ

# MCQ: Coordinate Geometry - 2 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Coordinate Geometry - 2

MCQ: Coordinate Geometry - 2 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Coordinate Geometry - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Coordinate Geometry - 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Coordinate Geometry - 2 below.
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MCQ: Coordinate Geometry - 2 - Question 1

### If the points A(4, 3)and B(x, 5) are on the circle with Centre O (2, 3). Find the value of x.

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 1

Since the two points A and B are on circle O, the distance between OA and OB will be equal.
Therefore, using the distance formula we get

Squaring both sides,
(x−2)2 + 4 = 4 therefore x = 2
Hence, x = 2 is the correct answer.

MCQ: Coordinate Geometry - 2 - Question 2

### If the distance between two points (0, -5) and (x,0) is 13 unit, then x equals to -

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 2

13​​​​​
= x2 + 25 = 169
= x2 = 169 - 25 = 144
∴ x = ±12

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MCQ: Coordinate Geometry - 2 - Question 3

### The equation of the line passing through (1, 2) and parallel to 3x + 4y + 7 = 0.

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 3

4y  =-3x-7

Since both lines are parallel,then slope will be same.

4y + 3x = 11

MCQ: Coordinate Geometry - 2 - Question 4

Suppose R is the region bounded by the two curves y = x2 and y = 2x− 1 as shown in the following diagram

Two distinct lines are drawn such that each of these lines partitions the regions into at least two parts. If 'n' is the total number of regions generated by these lines, then

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 4

According to the question, we are given a region bounded by the curves y = x2 and y = 2x− 1. The region is partitioned by drawing two distinct lines such that they divide the regions into two parts at least. The total number of regions, n, generated by these lines is unknown. To find the value of n we need to analyse the region.
Now, we draw the lines, as follows,

The two curves will meet when both the function have same value for any given x.

So, the equation will be x= 2x− 1.
On solving this equation we get
2x− x= 1x= 1x = ±1
So, from the above simplification, we got the points x = 1 and x = −1.
So, there is only one region bounded by the given curves, and if we partition this region using two lines we can have 4 or 5 regions based on how the lines are drawn.
Therefore, the value of 'n' can be 5 but not 6.

MCQ: Coordinate Geometry - 2 - Question 5

ax − 4y = −6 has a slope of  What is the value of a?

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 5

Given equation, ax − 4y = −6
Slope of the equation

a = -6

MCQ: Coordinate Geometry - 2 - Question 6

What is the distance between P(7, 4) and Q(3, 1)?

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 6

Using Distance formula

MCQ: Coordinate Geometry - 2 - Question 7

Find the distance between the points (−5,7) and (−1,3).

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 7

Given points: (– 5, 7) and (– 1, 3)
Distance between the points will be (x1, y1) and (x2, y2).
We know that,

Hence, the correct answer is 4√2.

MCQ: Coordinate Geometry - 2 - Question 8

The point of intersection of the line x + y + 1 = 0 and 2x – y + 5 = 0 is

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 8

x + y + 1 = 0 and 2x – y + 5 = 0
then x+y = -1, 2x-y=-5
by verification method, option :b (-2,1)
-2+1 = -1, -4-1 = -5

MCQ: Coordinate Geometry - 2 - Question 9

In the diagram AB || GH || DE and GF || BD || HI, ∠FGC = 80o, find the value of ∠CHI.

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 9

MCQ: Coordinate Geometry - 2 - Question 10

Find the ratio in which line 3x + 2y = 17 divides the line segment joined by points (2,5) and (5,2).

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 10

We assume that,

x1 = 2, y1 = 5, x2 = 5 & y2 = 2 Point C: (x,y)
Line divides the line segment in the ratio m1 : m2
This is known as internal division.

Point C satisfies the equation of line.

MCQ: Coordinate Geometry - 2 - Question 11

Let the vertices of a triangle ABC be (4, 4), (3, 5) and (−1,−1), then the triangle is:

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 11

The vertices of a triangle ABC be
(4, 4), (3, 5) and (−1,−1)
Distance between two points

Distance between

Distance between

Distance between

AC= 50
AB+ AC2 = 2 + 50 = 52
⇒ AB2 + AC2 = BC2
It follows Pythagoras theorem so, triangle is a right angle triangle.

MCQ: Coordinate Geometry - 2 - Question 12

Name the point of intersection in the given figure.

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 12

When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection.
Hence, the correct answer is O.

MCQ: Coordinate Geometry - 2 - Question 13

Find the value of z

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 13

From the given figure, we know that the sum of all the angles of a linear pair is always 180°. Here,  form a linear pair.

Hence, option B is the correct answer.

MCQ: Coordinate Geometry - 2 - Question 14

On the figure below, lines k and l are ∥.
The value of a° + b° is _______.

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 14

Given that,
∠BOA = 45°
∠AOD = a°
∠DOB = b°

Now, k || m || l
a°+b°=45° (given in question) as they form interior alternate angles with the transversal.
Hence, value of a°+b° is 45°.

MCQ: Coordinate Geometry - 2 - Question 15

The length of the intercept of the graph of the equation 9x − 12y = 108 between the two axis is -

Detailed Solution for MCQ: Coordinate Geometry - 2 - Question 15

equation  9x − 12y = 108
Intersection of y−axis (by putting x = 0)
−12y = 108
y = −9
intersection of x − axis(by putting y = 0)
9x = 108
x = 12

Using pythagoras theorm,
The length of the intercept is

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests