Question

Use the distance formula do to determine what type of triangle DEF is if it has coordinates D(2, 1), E(3, 5), F(6, 2). Just write the number you get under the square root symbols in the blank below in order.1. What is the length of DE2. What is the length of EF3. What is the length of DFList your answers for the above length of sides the name what type of triangle is DEF

Answer 1

Step 1

Draw the triangle DEF

Step 2

State the formula for the distance between two points

`D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)}^2`

Step 3

Find the length of DE

`\begin{gathered} DE=\sqrt[]{(3-2)^2+(5-1)^2} \\ DE=\sqrt[]{1^2+4^2} \\ DE=\sqrt[]{1+16} \\ DE=\sqrt[]{17} \end{gathered}`

Step 3

Find the length of EF

`\begin{gathered} EF=\sqrt[]{(6-3)^2+(2-5)^2} \\ EF=\sqrt[]{3^2+(-3)^2} \\ EF=\sqrt[]{9+9} \\ EF=\sqrt[]{18} \end{gathered}`

Step 4

Find the length of DF

`\begin{gathered} DF=\sqrt[]{(6-2)^2+(2-1)^2} \\ DF=\sqrt[]{4^2+1^2} \\ DF=\sqrt[]{16+1} \\ DF=\sqrt[]{17} \end{gathered}`

Step 5

Find out what type of triangle it is.

An isosceles triangle is a triangle that has two sides of equal length.

Since triangle DEF has lines DF and DE to be equal in length, we can conclude that triangle DEF is an Isosceles triangle