is triangle XYZ with vertices X(-3,1), Y(2.4), Z(2.-5) a scalene triangle?
A triangle XYZ has vertices X(1,1),Y(3,1),and Z(2,4).Find The equilateral triangle
what are the lengths of the sides?
If they are all different, it is scalene.
You can just do the squares of the lengths, no need to take the square roots.
in general:
length^2 = (X2-X1)^2 + (Y2-Y1)^2
for example the length from X to Y:
XY^2 = (2 - -3)^2 + (4 - 1)^2
= 5^2 + 3^2
= 25 + 9
= 34 is the square of length XY
To determine if triangle XYZ is a scalene triangle, you need to check if all three sides have different lengths.
To find the lengths of the sides, you can use the distance formula, which calculates the distance between two points in a coordinate plane:
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = √[(x2 - x1)² + (y2 - y1)²]
Let's calculate the lengths of the three sides of triangle XYZ:
Side XY:
d(XY) = √[(2 - (-3))² + (4 - 1)²]
= √[(2 + 3)² + (4 - 1)²]
= √[5² + 3²]
= √[25 + 9]
= √34
Side YZ:
d(YZ) = √[(2 - 2)² + (-5 - 4)²]
= √[0² + (-9)²]
= √[0 + 81]
= √81
= 9
Side XZ:
d(XZ) = √[(2 - (-3))² + (-5 - 1)²]
= √[(2 + 3)² + (-5 - 1)²]
= √[5² + (-6)²]
= √[25 + 36]
= √61
The lengths of the sides are approximately:
XY ≈ √34
YZ = 9
XZ ≈ √61
Since the lengths of all three sides are different, triangle XYZ is a scalene triangle.