is triangle RST with verticies R(-1,5), S(-4,1), T(2,1) a isosceles?
Again find the squares of the lengths of the sides. If two are the same it is.
To determine if triangle RST is isosceles, we need to compare the lengths of its sides. Recall that in an isosceles triangle, at least two sides have the same length.
To find the lengths of the sides, we can use the distance formula:
If two points have coordinates (x1, y1) and (x2, y2), the distance between them is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the lengths of the sides RS, ST, and RT using the given coordinates:
RS: Distance between R(-1, 5) and S(-4, 1)
= √((-4 - (-1))^2 + (1 - 5)^2)
= √((-3)^2 + (-4)^2)
= √(9 + 16)
= √25
= 5
ST: Distance between S(-4, 1) and T(2, 1)
= √((2 - (-4))^2 + (1 - 1)^2)
= √((6)^2 + (0)^2)
= √(36 + 0)
= √36
= 6
RT: Distance between R(-1, 5) and T(2, 1)
= √((2 - (-1))^2 + (1 - 5)^2)
= √((3)^2 + (-4)^2)
= √(9 + 16)
= √25
= 5
Now, we know that RS = RT = 5, but ST = 6. Since two sides (RS and RT) have the same length, while the third side (ST) has a different length, triangle RST is not isosceles.