Question

Use the distance formula three times to determine what type of triangle DEF is if it has coordinates D(2, 1), E(3, 5), and F(6, 2).

a) What is the length of DE? ________
b) What is the length of EF? _______
c) What is the length of DF? _______
d) What type of triangle is DEF, Scalene, Isosceles, or Equilateral? _______

Answer 1

To find the lengths of the sides of triangle DEF, we can use the distance formula. The lengths are sqrt(17), sqrt(18), and sqrt(17). Therefore, triangle DEF is a Scalene triangle.

Step-by-step explanation:

To find the length of each side of triangle DEF, we can use the distance formula. The distance formula is derived from the Pythagorean theorem. The formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

a) Using the formula, the length of DE is:

DE = sqrt((3 - 2)^2 + (5 - 1)^2) = sqrt(1 + 16) = sqrt(17)

b) The length of EF is:

EF = sqrt((6 - 3) ^ 2 + (2 - 5)^2) = sqrt(9 + 9) = sqrt(18)

c) The length of DF is:

DF = sqrt((6 - 2)^2 + (2 - 1)^2) = sqrt(16 + 1) = sqrt(17)

d) Triangle DEF is neither scalene, isosceles, nor equilateral because the lengths of all three sides are different. Therefore, it is a Scalene triangle.