Question

What type of triangle is formed by joining the points D(7, 3), E(8, 1), and F(4, -1)?

Answer 1

Answer:

This is an equilateral triangle.

Step-by-step explanation:

Given points :-

D ( 7,3) ,E (8,1) , F (4,-1)

Solution:-

Firstly find distance between D and E

$</u><u>DE</u><u>\: = \sqrt{ {(8 - 7)}^{2} + {( 1 - 3)}^{2} } \\ \\ </u><u>DE</u><u> = \sqrt{1 + 4} = \sqrt{5}$

Now ,find distance between E and F(EF)

$EF \: = \sqrt{ {( 4 - 8)}^{2} + {( - 1 - 1)}^{2} } \\ \\ EF = \sqrt{16 + 4} = \sqrt{20}$

Now find distance between F and D (FD)

$</u><u>FD</u><u> = \sqrt{ {(4 - 7)}^{2} + {( - 1 - 3)}^{2} } \\ \\ </u><u>FD</u><u> = \sqrt{9 + 16} = \sqrt{25 } \\ \\ </u><u>FD</u><u> = 5$

Now we have ,

${(</u><u>FD</u><u>)}^{2} = {(</u><u>DE</u><u>)}^{2} + {(</u><u>EF</u><u>)}^{2} \\ \\ 25 = 20 + 5 \\ \\ 25 = 25$

Hence , this is an equilateral triangle.