Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202419 May 2024Evening ShiftMathematicsStraight LinesActual

Point (-1,2) is changed to ( a , b ) when the origin is shifted to the point (2,-1) by translation of axes, Point (a, b) is changed to (c, d) when the axes are rotated through an angle of 45^ about the new origin. (c, d) is changed to ( e , f) when (c, d) is reflected through y=x . Then (e, f)=

Options

  1. A(-3,3)
  2. B(0,3 2 )
  3. C(3 2 , 0)
  4. D(1,2)

Correct answer

C. (3 2 , 0)

Step-by-step solution

Since, after translation So, a=-1-2=-3, b=2-(-1)=3 (a, b)=(-3,3) Since, =45^ c=-3 (45^ )+3 (45^ )= -3 2 + 3 2 =0 and d=-(-3) (45^ )+3 (45^ )= 3 2 + 3 2 =3 2 So, (c, d)=(0,3 2 ) Now, reflection of point (0,3 2 ) about y=x is (e, f)=(3 2 , 0) .

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All AP EAMCET PYQs