alleryStart learning →Axes are moved so the new origin is (-1, 4). Find the new coordinates of (3, 2).
- (4, -2)
- (2, 6)
- (4, 2)
- (-4, 2)
Show answer and solution
Correct answer: A. (4, -2)
Subtract the origin shift: (3 + 1, 2 - 4) = (4, -2).
AP EAMCET Coordinate Geometry: Transformation of Axes — practice questions
Explore 51 free Coordinate Geometry: Transformation of Axes questions in AP EAMCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 51.
Axes are moved so the new origin is (-1, 4). Find the new coordinates of (3, 2).Read the answer and worked solution →After shifting the origin to (1, 2), a point has new coordinates (4, 5). Its old coordinates areRead the answer and worked solution →Origin shifted to (2, -1). What does y = 2x + 3 become in the new axes?Read the answer and worked solution →Shifting the origin to (1, 1) turns x² + y² - 2x - 2y - 2 = 0 intoRead the answer and worked solution →Moving the origin to (2, 2) reduces y² - 4y - 8x + 20 = 0 to which form?Read the answer and worked solution →To remove the first-degree terms of x² + y² + 6x - 8y = 0, move the origin toRead the answer and worked solution →The origin should be moved to which point to remove x and y terms of 3x² + 2y² - 6x + 8y - 1 = 0?Read the answer and worked solution →When axes are translated, the coefficients of x², xy and y² in a second-degree equationRead the answer and worked solution →Which statement holds for a translation of axes in the plane?Read the answer and worked solution →Which is true of a rotation of axes about the origin?Read the answer and worked solution →Axes are shifted 3 units right and 2 units up. A fixed point P then appears movedRead the answer and worked solution →If the axes are rotated counterclockwise through an angle, a fixed point appears rotatedRead the answer and worked solution →A rotation of axes in a second-degree equation is chosen to eliminate theRead the answer and worked solution →After the xy term is gone, a translation of axes removes which terms?Read the answer and worked solution →Which algebraic method is used with a translation to simplify a conic equation?Read the answer and worked solution →In 3D, a new origin for a translation of axes is given by how many coordinates?Read the answer and worked solution →A second-degree equation in x, y, z that is not a cylinder, plane, line or point gives aRead the answer and worked solution →Axes are rotated 90° counterclockwise. The point (3, 4) gets new coordinatesRead the answer and worked solution →After the axes turn through 180°, the point (3, -5) has coordinatesRead the answer and worked solution →After a 90° counterclockwise axes rotation, a point is (2, 5) in the new system. Originally it wasRead the answer and worked solution →Rotating the axes by 45° changes 3x² + 2xy + 3y² = 8 intoRead the answer and worked solution →The curve xy = 8 is rotated by turning the axes through 45°. Its new equation isRead the answer and worked solution →The curve 2x² + xy + 3y² = 6 is of which type?Read the answer and worked solution →The curve x² + 3xy + y² = 5 is aRead the answer and worked solution →The curve 4x² + 4xy + y² + 2x = 0 represents aRead the answer and worked solution →For axes rotated counterclockwise by θ, the old x equalsRead the answer and worked solution →The point (3, 4) is distance D from the origin. After any rotation of axes, D isRead the answer and worked solution →In a shift of origin to (h, k), the new x' axis is parallel to x and lies how far away?Read the answer and worked solution →In a translation of axes, the positive x' and y' directions are taken to beRead the answer and worked solution →The ellipse (x - 2)²/9 + (y + 1)²/4 = 1 takes standard form with origin atRead the answer and worked solution →
Worked practice questions
After shifting the origin to (1, 2), a point has new coordinates (4, 5). Its old coordinates are
- (5, 7)
- (3, 3)
- (-3, -3)
- (4, 5)
Show answer and solution
Correct answer: A. (5, 7)
Old coordinates are x = x' + h and y = y' + k, giving (4 + 1, 5 + 2) = (5, 7).
Origin shifted to (2, -1). What does y = 2x + 3 become in the new axes?
- y' = 2x' - 8
- y' = 2x' + 4
- y' = 2x' + 6
- y' = 2x' + 8
Show answer and solution
Correct answer: D. y' = 2x' + 8
Put x = x' + 2 and y = y' - 1, so y' - 1 = 2x' + 7, which gives y' = 2x' + 8.
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