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Test: Shifting Of Origin - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Shifting Of Origin

Test: Shifting Of Origin for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Shifting Of Origin questions and answers have been prepared according to the JEE exam syllabus.The Test: Shifting Of Origin MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Shifting Of Origin below.
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Test: Shifting Of Origin - Question 1

The origin lies on

Detailed Solution for Test: Shifting Of Origin - Question 1

The origin lies on the intersection of X-axis and Y-axis. So, it lies on both the axes.

Test: Shifting Of Origin - Question 2

What will be the new equation of the straight line 3x + 4y = 15, if the origin gets shifted to (1,-3) ?

Detailed Solution for Test: Shifting Of Origin - Question 2

 Equation : 3x + 4y = 15
Points : (1,-3)
3(x-1) + 4(y-(-3)) = 15
3(x-1) + 4(y+3) = 15
3x - 3 + 4y + 12 = 15
3x + 4y = 6

Test: Shifting Of Origin - Question 3

What will be the new equation of the straight line 5x + 8y = 10, if the origin gets shifted to (2,-3) ?

Detailed Solution for Test: Shifting Of Origin - Question 3

Equation : 5x + 8y = 10
Points (2, -3)
(x-2, y+3)
⇒ 5(x-2) + 8(y+3) = 10
= 5x - 10 + 8y + 24 = 10
⇒ 5x + 8 = - 4

Test: Shifting Of Origin - Question 4

The point where all the angle bisectors of a triangle meet is

Detailed Solution for Test: Shifting Of Origin - Question 4

The angle bisectors of the angles of a triangle are concurrent (they intersect in one common point). The point of concurrency of the angle bisectors is called the incenter of the triangle.

Test: Shifting Of Origin - Question 5

What will be the new equation of the straight line 5x + 8y = 10, if the origin gets shifted to (2,-3) ?

Test: Shifting Of Origin - Question 6

What will be the value of ‘p” if the equation of the straight line 3x + 5y = 10 gets changed to 3x + 5y = p after shifting the origin at (2,2) ?

Detailed Solution for Test: Shifting Of Origin - Question 6

3x + 5y = 10, at origin
But now, it’s (2,2),
3(x-2) + 5(y-2) = 10
Hence, 3x - 6 + 5y - 10 = 10
3x + 5y = 26
So, 3x + 5y = p
=> p = 26.

Test: Shifting Of Origin - Question 7

If area of ΔABC = 0 ,three points A,B,C are

Detailed Solution for Test: Shifting Of Origin - Question 7

The three points A, B and C are collinear if and only if area of ΔABC = 0.

Test: Shifting Of Origin - Question 8

The distance between the pair of points (7,8) and (4,2) ,if origin is shifted to (1,-2) ,would be

Detailed Solution for Test: Shifting Of Origin - Question 8

Test: Shifting Of Origin - Question 9

The coordinates of centroid of triangle whose vertices are A(-1,-3), B(5,-6) and C(2,3) and origin gets shifted to (1,2) 

Detailed Solution for Test: Shifting Of Origin - Question 9

Midpoint = ((x1 + x2) / 2 , (y1 + y2) / 2) where (x1, y1) and (x2, y2) are the coordinates of the endpoints. Finding the Coordinates of the Centroid: Once we have the midpoints of each side, we can find the equation of the three medians and then find their intersection point. The intersection point is the centroid of the triangle. Let's find the midpoint of each side first: Midpoint of AB = ((-1 + 5) / 2 , (-3 - 6) / 2) = (2, -4.5) Midpoint of AC = ((-1 + 2) / 2 , (-3 + 3) / 2) = (0.5, 0) Midpoint of BC = ((5 + 2) / 2 , (-6 + 3) / 2) = (3.5, -1.5) Now we can find the equation of the medians. The equation of a line that passes through two points (x1, y1) and (x2, y2) is: (y - y1) / (y2 - y1) = (x - x1) / (x2 - x1) Let's find the equation of the median that passes through A: Midpoint of BC = (3.5, -1.5) Slope of BC = (-6 - 3) / (5 - 2) = -3 Equation of BC: y + 6 = -3(x - 5) => y = -3x + 21 Slope of median from A to BC = (3 - (-3)) / (2 - 5) = 2/3 Equation of median from A to BC: y + 3 = (2/3)(x + 1) => y = (2/3)x + (5/3) Similarly, we can find the equations of the medians that pass through B and C: Equation of median from B to AC: y + 6 = (1/3)(x - 5) => y = (1/3)x + 11/3 Equation of median from C to AB: y - 3 = (-2/3)(x - 2) => y = (-2/3)x + 5/3 Now we need to find the intersection point of these three medians. We can solve the system of equations: y = (2/3)x + (5/3) y = (1/3)x + 11/3 y = (-2/3)x + 5/3 Solving these equations, we get x = -1 and y =4

Test: Shifting Of Origin - Question 10

New coordinates of the point (7,-1) would be, if the origin is shifted to the point (1,2) by translation of the axis.

Detailed Solution for Test: Shifting Of Origin - Question 10

 Let the new origin be (h, k) = (1, 2) and (x, y) = (7, -1) be the given point
Therefore new co-ordinates (X, Y) .
x = X + h and y = Y + k
i.e. 7 = X + 1 and -1 = Y + 2
This gives, X = 6 and Y = -3.
Thus the new co-ordinates are (6, -3)

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