Trapezoid DEFG has vertices D (1,3), E (5,3), F (7,-1) and G (1, -1). Imagine the image D' E' F' G' after a 90 degree (counterclockwise) rotation about the origin. Enter the coordinate of E'.

Question

E is located at ( __, __)

Answer 1

To find the coordinates of point E after a 90-degree counterclockwise rotation about the origin, we can use the following transformation rule for rotation:

For a point \((x, y)\), the coordinates after a 90-degree counterclockwise rotation are given by the formula: \[ (x', y') = (-y, x) \]

Given the coordinates of point E are \( (5, 3) \):

Applying the transformation:

• The new x-coordinate \( x' = -y = -3 \)
• The new y-coordinate \( y' = x = 5 \)

Therefore, the coordinates of point E' after the rotation are \( (-3, 5) \).

So, the coordinate of E' is: \[ E' = (-3, 5) \]