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All questions of Coordinate Geometry for SSC CGL Exam
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?- a)8
- b)-8
- c)6
- d)-6
Correct answer is option 'B'. Can you explain this answer?
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?
a)
8
b)
-8
c)
6
d)
-6
 | Ssc Cgl answered |
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:
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:
The equation of the line passing through (1, 2) and parallel to 3x + 4y + 7 = 0.- a)3x – 4y = 11
- b)3x + 4y =11
- c)3x + 4y = 0
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The equation of the line passing through (1, 2) and parallel to 3x + 4y + 7 = 0.
a)
3x – 4y = 11
b)
3x + 4y =11
c)
3x + 4y = 0
d)
None of these
| | Ssc Cgl answered |
- The given line is:
- 3x + 4y + 7 = 0
- Step 1: Find the slope of the given line:
- Rewrite as y = mx + c: y = -3/4 * x - 7/4
- So, the slope (m) is: -3/4.
- Step 2: Use the point-slope form for the new line passing through (1, 2):
- y - 2 = -3/4 (x - 1)
- Step 3: Simplify the equation:
- y - 2 = -3/4 * x + 3/4 y = -3/4 * x + 3/4 + 2 y = -3/4 * x + 11/4
- Step 4: Convert to general form:
- Multiply by 4: 4y = -3x + 11 Rearrange: 3x + 4y = 11
The point of intersection of the line x + y + 1 = 0 and 2x – y + 5 = 0 is- a)(–1, 1)
- b)(–2, 1)
- c)(1, 2)
- d)(1, –2)
Correct answer is option 'B'. Can you explain this answer?
The point of intersection of the line x + y + 1 = 0 and 2x – y + 5 = 0 is
a)
(–1, 1)
b)
(–2, 1)
c)
(1, 2)
d)
(1, –2)
| | Ssc Cgl answered |
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
then x+y = -1, 2x-y=-5
by verification method, option :b (-2,1)
-2+1 = -1, -4-1 = -5
What is the reflection on the point (−4, 3) in the line x = −2?- a)(−4, −7)
- b)(4, 3)
- c)(0, 3)
- d)(−4, 7)
Correct answer is option 'C'. Can you explain this answer?
What is the reflection on the point (−4, 3) in the line x = −2?
a)
(−4, −7)
b)
(4, 3)
c)
(0, 3)
d)
(−4, 7)
 | Abhiram Mehra answered |
Understanding Reflection Across a Vertical Line
When reflecting a point across a vertical line, the x-coordinate will change, while the y-coordinate remains the same. In this case, we are reflecting the point (-4, 3) across the line x = -2.
Steps to Find the Reflection:
1. Identify the Original Point and Line of Reflection:
- Original Point: (-4, 3)
- Line of Reflection: x = -2
2. Calculate the Distance from the Point to the Line:
- The original point's x-coordinate is -4.
- The distance to the line x = -2 is:
- Distance = -2 - (-4) = 2 units.
3. Reflecting the Point:
- To find the reflection, we move the same distance (2 units) on the opposite side of the line.
- New x-coordinate: -2 + 2 = 0.
- The y-coordinate remains unchanged: 3.
4. Resulting Coordinates of the Reflection:
- The reflected point is (0, 3).
Conclusion:
The correct reflection of the point (-4, 3) in the line x = -2 is (0, 3). Therefore, the correct answer is option 'C'.
When reflecting a point across a vertical line, the x-coordinate will change, while the y-coordinate remains the same. In this case, we are reflecting the point (-4, 3) across the line x = -2.
Steps to Find the Reflection:
1. Identify the Original Point and Line of Reflection:
- Original Point: (-4, 3)
- Line of Reflection: x = -2
2. Calculate the Distance from the Point to the Line:
- The original point's x-coordinate is -4.
- The distance to the line x = -2 is:
- Distance = -2 - (-4) = 2 units.
3. Reflecting the Point:
- To find the reflection, we move the same distance (2 units) on the opposite side of the line.
- New x-coordinate: -2 + 2 = 0.
- The y-coordinate remains unchanged: 3.
4. Resulting Coordinates of the Reflection:
- The reflected point is (0, 3).
Conclusion:
The correct reflection of the point (-4, 3) in the line x = -2 is (0, 3). Therefore, the correct answer is option 'C'.
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