MCQ: Coordinate Geometry - 1 - SSC CGL MCQ

# MCQ: Coordinate Geometry - 1 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Coordinate Geometry - 1

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

### The centroid of the triangle whose vertices are (3, 10), (7, 7), (− 2, 1) is:

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

According to the question,

Centroid of the triangle

Hence, the correct option is

MCQ: Coordinate Geometry - 1 - Question 2

### Find the y-intercept of the line joining two points (1,3) and (3,5)?

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

The equation of the line passing through the points, (1, 3) and (3, 5)
We know the two-point form of a line passing through these two points is:

As the intercept form is represented as

Hence, the y-intercept is 2.

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MCQ: Coordinate Geometry - 1 - Question 3

### What is the reflection on the point (−4, 3) in the line x = −2?

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 3

Coordinates of the point is (−4, 3).
Since, we need to find the reflection along x = −2, the y-coordinate remains unaffected.
Now, for reflection, the distance from the line of the reflection to the object should be equal to the distance to the image point.
So, for x-coordinate:
If the distance from the image to the line of reflection is 'A' and the distance from the object to the line of reflection be 'B'.
And, X1 be the x coordinate of point (−4, 3).

Hence, the correct answer is (0, 3).

MCQ: Coordinate Geometry - 1 - Question 4

The distance of point (−2, 3) from the line x − y = 5 is:

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 4

According to the problem,
The equation of the line is x − y = 5 or x − y − 5 = 0
Point(P) = (−2, 3)
Distance

Hence, the distance is 5√2.

MCQ: Coordinate Geometry - 1 - Question 5

Find the co-ordinates of the centroid of a triangle whose vertices are (0, 6) (8, 12) and (8, 0)?

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 5

Let the coordinates of the centroid be  (x, y).
x-axis coordinates of the centroid

y-axis coordinates of the centroid

So, Coordinates of centroid is

MCQ: Coordinate Geometry - 1 - Question 6

If the sum of the diagonal elements of a 2 × 2 matrix is −6, then the maximum possible value of determinant of the matrix is ________.

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 6

Let the matrix be

The determinant is:
It is given that,
a + d = −6d = −6 − a  −(1)
For maximum value, bc = 0
Then,
|A| = a(−6−a)|A| = −6a−a2
Differentiating both sides w.r.t. a we get,

It has maximum value at a = −3
d = −6−ad = −6−(−3)d = −3
So, maximum value is:

Hence, the required answer is 9.

MCQ: Coordinate Geometry - 1 - Question 7

Perform the following operations on the matrix

(i) Add the third row to the second row
(ii) Subtract the third column from the first column.
The determinant of the resultant matrix is ___________.

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 7

The given matrix is:

According to question,
(i) On adding the third row to the second row we get,

(ii) Subtract the third column from the first column we get,

It is clear that,
Third column=14×first column
So, the determinant will be zero as third coulmn is multiple of first column.
Hence, the required answer is 0.

MCQ: Coordinate Geometry - 1 - Question 8

Point A(4, 2) divides segment BC in the ratio 2 : 5. Coordinates of B are (2, 6) and C is (7, y). What is the value of y?

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 8

The coordinates of A are (4, 2).
The coordinates of B are (2, 6).
The coordinates of C are (7, y).
x1 = 2, x2 = 7, y1 = 6, y2 = y, m1 = 2, m2 = 5
By using the section formula:

MCQ: Coordinate Geometry - 1 - Question 9

Find the intercepts made by the line 2x – 3y + 6 = 0 with the coordinate axes.

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 9

2x – 3y + 6 = 0

then it is in the format of
The intercepts are -3, 2

MCQ: Coordinate Geometry - 1 - Question 10

Point P is the mid-point of segment AB. Coordinates of P are (3,1) and B are (5, −4). What are the coordinates of point A?

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 10

According to Mid−Point Formula,

(xm, ym) are the coordinates of mid−point.

(x1, y1) are the coordinates of first point.

(x2, y2) are the coordinates of second point.
Given, coordinates of mid−point P = (3,1).
coordinates of second point B = (5, −4)
Let the coordinates of first point A (x1, y1).
Now, on using mid−point formula, we get

MCQ: Coordinate Geometry - 1 - Question 11

If p and q are reciprocal to each other and p = (5 + 2√6), then what will be the value of q?

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 11

Therefore,

Hence, the value of q is (5 − 2√6).

MCQ: Coordinate Geometry - 1 - Question 12

AB ∥ CD and the line EF cuts these lines at the points M and N respectively. Bisectors of angles ∠BMN and ∠MND meet at the point Q. Find the value of ∠MQN.

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 12

∠BMN + ∠DNM = 180o (consecutive interior angles)

MCQ: Coordinate Geometry - 1 - Question 13

Find the value of k for which the lines 5x + 3y + 2 = 0 and 3x − ky + 6 = 0 are perpendicular.

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 13

The slope is the measure of the rise (or change in the y-axis) over the run (or change in the x-axis).
Let slope of lines are m1 and m2 respectively

When lines are perpendicular, then m1 × m2 = −1

k = 5

MCQ: Coordinate Geometry - 1 - Question 14

In the given diagram, TU || PS and points Q and R lie on PS. Also, ∠PQT = x°, ∠RQT = (x − 50)° and ∠TUR = (x + 25)°. What is the measure of ∠URS?

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 14

It is given that,∠PQT = x°, ∠RQT = (x − 50)° & ∠TUR = (x + 25)°
We can write as,
∠PQT + ∠RQT = 180°
x+(x−50) = 180°
2x = 230
x = 115°
Also, we can write as,
∠TUR+∠URQ = 180°
(115+25)+∠URQ = 180°
∠URQ = 180 − 140 = 40°
Therefore,
∠URS = 180 −∠URQ
∠URS = 180 − 40 = 140°

MCQ: Coordinate Geometry - 1 - Question 15

The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is?

Detailed Solution for MCQ: Coordinate Geometry - 1 - Question 15

Straight line = 3x + 4y = 12
General intercepted form of straight line
This straight-line is written as-

Comparing (1) and (2),
a = 4 and b = 3
Therefore, the required length

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests