triangle pqr id drawn with the coordinates p(0,2) q(0,5) r(1,4) determine the translation direction and number of units if r' (-7,4)

Answer 1

To determine the translation direction and number of units for point \( R(1, 4) \) to \( R'(-7, 4) \), we can follow these steps:

1. Identify the original coordinates of point R:

   • \( R(1, 4) \)

2. Identify the coordinates of the translated point R':

   • \( R'(-7, 4) \)

3. Calculate the translation vector:

   • The translation vector can be found by subtracting the coordinates of \( R \) from \( R' \): \[ \text{Translation vector} = R' - R = (-7, 4) - (1, 4) \]

   This gives us: \[ \text{Translation vector} = (-7 - 1, 4 - 4) = (-8, 0) \]

4. Interpret the results:

   • The translation vector \( (-8, 0) \) means that the point \( R \) has moved 8 units to the left (in the negative x-direction) and 0 units in the y-direction.

5. Conclusion:

   • The translation direction is 8 units to the left, and there is no vertical movement.