Question

Tropical Smoothie is halfway between Shawn's house and Isabella's houseShawn's house is located at the point (4, 6) on the coordinate plane, and Tropical Smoothie is located at the point (8, 3) Find the coordinates of Isabella's house

Answer 1

To find Isabella's house coordinates, the midpoint formula is used in reverse. Starting from the midpoint coordinates (8, 3) and Shawn's coordinates (4, 6), it is determined that Isabella's house is at (12, 3).

Step-by-step explanation:

The question is asking to find the coordinates of Isabella's house if Tropical Smoothie is halfway between Shawn's house and Isabella's house. Given that Shawn's house is at (4, 6) and Tropical Smoothie is at (8, 3), we can find Isabella's house by using the midpoint formula in reverse. Since Tropical Smoothie is at the midpoint, it will have the coordinates that are the average of the coordinates of Shawn's and Isabella's houses. The formula for the x-coordinate of the midpoint is (x1 + x2) / 2, and for the y-coordinate is (y1 + y2) / 2. Since we know the midpoint's x-coordinate is 8 and the y-coordinate is 3, we can set up two equations:

(4 + x2) / 2 = 8
(6 + y2) / 2 = 3

Solving these equations:

• x2 = 16 - 4
• x2 = 12

• y2 = 6 - 3
• y2 = 3

Thus, the coordinates for Isabella's house would be (12, 3).