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Zorluk: KolayTransformations in the Coordinate Plane

A digital graphic designer positions a control point of a logo at the coordinates (−4,1)(-4, 1) on a computer screen's coordinate grid. The designer then translates the logo so that the control point moves 33 units to the left and 66 units up. What are the coordinates of the control point in its new position?

  1. A
    (−1,7)(-1, 7)
  2. (−7,7)(-7, 7)Cevap
  3. C
    (−7,−5)(-7, -5)
  4. D
    (−1,−5)(-1, -5)
  5. E
    (−10,4)(-10, 4)

Cevap

The correct coordinates of the control point in its new position are (−7,7)(-7, 7).
To find the coordinates of the image after a translation, adjust the original coordinates based on the direction of movement. Since the point starting at (−4,1)(-4, 1) is translated 33 units to the left, subtract 33 from the xx-coordinate: −4−3=−7-4 - 3 = -7. Since it is translated 66 units up, add 66 to the yy-coordinate: 1+6=71 + 6 = 7. This gives the final coordinates of (−7,7)(-7, 7).

Adım Adım Çözüm

1
Identify the initial coordinates of the point and the translation instructions.
Initial coordinates are (x,y)=(−4,1)(x, y) = (-4, 1). The translation is 33 units to the left and 66 units up.
This establishes the starting point and the transformation rules that need to be applied.
2
Apply the horizontal translation to the xx-coordinate.
x′=−4−3=−7x' = -4 - 3 = -7
Translating a point to the left on the coordinate plane decreases its xx-value, so we subtract 33 from the initial xx-coordinate.
3
Apply the vertical translation to the yy-coordinate.
y′=1+6=7y' = 1 + 6 = 7
Translating a point upward on the coordinate plane increases its yy-value, so we add 66 to the initial yy-coordinate.

Anahtar Kavram

Applying translations to coordinate points by adding or subtracting units from the xx- and yy-coordinates depending on the direction of movement.
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Konular

Transformations in the Coordinate Plane

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