Final answer:
To find the coordinates of the third vertex Y in triangle XYZ, we can use the formula for the area of a triangle. Given that the area is 10 units² and the base is the distance between X and Z, which is 4 units, we can solve for the height and then find the coordinate of Y. Therefore, the coordinates of the third vertex Y are (1, 0).
Step-by-step explanation:
To find the coordinates of the third vertex Y in triangle XYZ, we can use the formula for the area of a triangle.
The formula is:
Area = 1/2 * base * height
Given that the area is 10 units² and the base is the distance between X and Z, which is 4 units, we can solve for the height and then find the coordinate of Y.
Height = 2 * Area / base = 2 * 10 / 4 = 5
The coordinates of X are (1, 5) and Z are (1, 1). The x-coordinate of Y is the same as X, which is 1. The y-coordinate of Y can be found by subtracting the height from the y-coordinate of X: 5 - 5 = 0.
Therefore, the coordinates of the third vertex Y are (1, 0).