What kind of triangle is made by connecting the points A( -6)B(3,-6) and C(3,- 2) ?
To determine the kind of triangle formed by connecting the points A(-6), B(3, -6), and C(3, -2), we need to calculate the lengths of all three sides of the triangle using the distance formula.
Distance between A(-6) and B(3, -6):
dAB = √((x2-x1)^2 + (y2-y1)^2)
= √((3-(-6))^2 + (-6-(-6))^2)
= √((3+6)^2 + (-6+6)^2)
= √(9^2 + 0^2)
= √81
= 9
Distance between B(3, -6) and C(3, -2):
dBC = √((x2-x1)^2 + (y2-y1)^2)
= √((3-3)^2 + (-2-(-6))^2)
= √(0^2 + 4^2)
= √(16)
= 4
Distance between C(3, -2) and A(-6):
dCA = √((x2-x1)^2 + (y2-y1)^2)
= √((-6-3)^2 + (-2-(-6))^2)
= √((-9)^2 + 4^2)
= √(81 + 16)
= √(97)
Now, let's analyze the lengths of these three sides:
Side AB: 9
Side BC: 4
Side CA: √97
Since all three sides have different lengths, this triangle does not fit any of the properties of a specific kind of triangle (equilateral, isosceles, or scalene). Therefore, we would categorize this triangle as a scalene triangle.