Ms. chu plotted the points (4,3) and (-1,3) on a coordinates plane. the points are vertices of a right triangle with an area of 15 square units. what could be the coordinates of the third vertex?

Formula for the area of a triangle is 1/2bh
b=distance between the two points you gave.
distance between (4,3) and (-1,3) is 5.
1/2 * 5 * h = 15 square units
2.5 * h = 15 square units
h=6
This means the right triangle can be any point that is 6 units higher or lower than the two points you gave.

One of the answers to the question is (4,9). This is because the y value for the point (4,3) was changed by 6. Another possible answer is (4,-3) since distance cannot be negative, so it is still 6 units away from the point (4,3)

To find the third answer add 6 to the y value of (-1,3). The fourth answer can be found by subtracting 6 from the y value of (1,-3). Hope this helps.