Question

Prove or disprove the triangle with vertices R (−2, −2), S (1, 4), and T (4, -5) is an equilateral triangle.​

Answer 1

Answer:

The distance between two points formula = √[(x2-x1)^2+(y2-y1)^2]

1) distance between R and S is

√[((1-(-2))^2)+((4-(-2))^2] = √[(1+2)^2+(4+2)^2]

= √(3^2+6^2)

= √(9+36)

= √45=3√5

2) distance between R and T is

√[((4-(-2))^2)+((-5-(-2))^2] = √[(4+2)^2+(-5+2)^2]

= √(6^2+(-3)^2)

= √(36+9)

= √45=3√5

3) distance between S and T is

√[((4-1)^2)+((-5-4)^2] = √[(3)^2+(-9)^2]

= √(9+81)

= √90=3√10

Only two sides are equal, so traingle RST is not an equilateral triangle.