Final answer:
The area of triangle RST with vertices (1,2), (5,2), and (7,10) is found using the formula 1/2 × base × height. With a base of 4 units and a height of 8 units, the triangle's area is 16 square units.
Step-by-step explanation:
To find the area of a triangle with vertices (1,2), (5,2), and (7,10), we can use the formula for the area of a triangle, which is 1/2 × base × height. In this case, the base of the triangle can be the horizontal distance between the points (1,2) and (5,2), which is 4 units. The height can be considered as the vertical distance from the point (7,10) to the line formed by points (1,2) and (5,2), which is 8 units (from y=2 to y=10).
The area is then calculated as follows:
Area = 1/2 × base × height
Area = 1/2 × 4 × 8
Area = 2 × 8
Area = 16 square units
Therefore, the area of triangle RST is 16 square units.