Question

If point F at coordinates (2,4) is translated 6 units up and 3 units left to create point A, and vertex S is at coordinates (1,3), then what are the coordinates of vertex A?

A) (9,1)
B) (5,7)
C) (8,0)
D) (2,4)

Answer 1

The correct answer is option B) (5,10), obtained by translating point F at (2,4) six units up and three units left to reach the new coordinates for vertex A.

Step-by-step explanation:

The correct answer is option B) (5,10). To determine the coordinates of vertex A after the translation of point F, we perform the given transformations on point F's coordinates. Point F is at (2,4), and we are translating it 6 units up and 3 units left. Translating a point up means increasing its y-coordinate, while translating it left means decreasing its x-coordinate.

To find the coordinates of vertex A, we need to apply the given translation to point F. Since we are translating 6 units up and 3 units left, we subtract 6 from the y-coordinate of F and subtract 3 from the x-coordinate of F.

Therefore, the coordinates of vertex A are (2 - 3, 4 - 6), which simplifies to ( - 1, - 2). So, option B) (5,7) is the correct choice.

So, the translation 6 units up from (2,4) gives us (2, 4+6) which simplifies to (2,10). Then translating 3 units left gives us (2-3, 10) which simplifies to (5,10). Therefore, the new coordinates for point A after the translation are (5,10).