Question

The coordinates of the vertices of △RST are R(-3, 1), S(-1, 4), and T(3, 1). Which statement correctly describes whether △RST is a right triangle?

a) △RST is a right triangle because RS¯¯¯¯¯ is perpendicular to RT¯¯¯¯¯.
b) △RST is a right triangle because segment RS is perpendicular to segment RT.
c) △RST is not a right triangle because no two sides are perpendicular.
d) △RST is a right triangle because ST¯¯¯¯¯ is perpendicular to RT¯¯¯¯¯.

Answer 1

To determine if triangle RST is a right triangle, we need to check if any of the sides of the triangle are perpendicular to each other. The slopes of the sides SR and RT are not negative reciprocals of each other, so △RST is not a right triangle.

Step-by-step explanation:

To determine if triangle RST is a right triangle, we need to check if any of the sides of the triangle are perpendicular to each other. We can find the slope of the lines formed by the sides of the triangle and check if they are negative reciprocals of each other. Let's calculate the slopes:

SR: (4 - 1) / (-1 - (-3)) = 3 / 2
RT: (1 - 4) / (3 - (-1)) = -3 / 4

The slopes are not negative reciprocals of each other, so △RST is not a right triangle. Therefore, the correct statement is c) △RST is not a right triangle because no two sides are perpendicular.