Question

Triangle SUB has vertices S(-3,-1), U(0,3), and B(4,-2). Using coordinate geometry, prove that the triangle SUB is scalene.

a) The lengths of all sides are equal.
b) Two angles are equal.
c) All angles are equal.
d) All sides are of different lengths.

Answer 1

d) All sides are of different lengths.. To prove that triangle SUB is scalene, we can calculate the lengths of its sides using coordinate geometry. By calculating the lengths of sides SU, US, and SB, we can show that they are all different. Therefore, triangle SUB is scalene.

Step-by-step explanation:

To prove that triangle SUB is scalene, we need to show that all sides have different lengths. By using coordinate geometry, we can calculate the lengths of the sides. Let's start with side SU. Using the distance formula, we can find the length of SU by finding the distance between points S and U:

Length of SU = sqrt((0 - (-3))^2 + (3 - (-1))^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5

Similarly, we can calculate the lengths of the other sides:

Length of US = sqrt((0 - 4)^2 + (3 - (-2))^2) = sqrt((-4)^2 + 5^2) = sqrt(16 + 25) = sqrt(41)

Length of SB = sqrt((-3 - 4)^2 + (-1 - (-2))^2) = sqrt((-7)^2 + 1^2) = sqrt(49 + 1) = sqrt(50) = 5sqrt(2)

Since the lengths of the sides SU, US, and SB are all different, triangle SUB is scalene. Therefore, the correct option is (d) All sides are of different lengths.