Question

Determine whether or not the given points form a right triangle if the triangle is not a right triangle, determine if it is ISOSCELES or SCALENE

Answer 1

We are given three points: (6, 3), (4, 9), and (8, 9).

To find out if they form a triangle, and if they do, what kind, we will be using the distance formula. This will tell us the length of each line segment (side of the triangle, if any triangle is formed).

The formula to find the distance between two points is:

`d=√((x_1-x_2)^2+(y_1-y_2)^2)`

Let's solve for the lengths of the sides.

`\begin{gathered} d_1=√((6-4)^2+(3-9)^2) \\ d_1=√(4+36) \\ d_1=√(40) \\ d_1=2√(10) \end{gathered}`
`\begin{gathered} d_2=√((6-8)^2+(3-9)^2) \\ d_2=√(4+36) \\ d_2=√(40) \\ d_2=2√(10) \\ \end{gathered}`
`\begin{gathered} d_3=√((4-8)^2+(9-9)^2) \\ d_3=√(16+0) \\ d_3=4 \end{gathered}`

We now know that 2 sides have the same measurement, 2 sqrt 10, while the third side measures 4 units.

Therefore, the triangle formed is isosceles.

Also, we can check that the triangle is NOT right by using the Pythagorean Theorem: