Final answer:
The area of the triangle with given vertices is 10 square units, calculated using the distance between points to find the base and height, and then applying the formula for the area of a triangle.
Step-by-step explanation:
The question asks for the area of a triangle with vertices at coordinates ( -1, 1 ), ( -1, 5 ), and ( 4 ,1 ). To compute this, we can use the formula for the area of a triangle that uses the base and height.
Notice that the points ( -1, 1 ) and ( -1, 5 ) form a vertical line, indicating the height of the triangle is the distance between the y-coordinates, which is 5 - 1 = 4 units.
Similarly, the base can be found by the distance between the x-coordinates of ( -1, 1 ) and ( 4, 1 ), which is 4 - (-1) = 5 units. The area of the triangle is then given by:
Area = ½ × base × height
Thus:
Area = ½ × 5 × 4 = 10 square units.