Question

The vertices of ABC are A (2,6) B(0,2) C (3,3). What type of triangle is ABC

Answer 1

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Answer 2

we are given

three vertices as

A (2,6) B(0,2) C (3,3)

now, we can draw these vertices and find triangle

we can use distance formula

and find AB , BC and AC

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Calculation of AB:

We can use formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

A (2,6) B(0,2)

`AB=√((0-2)^2+(6-2)^2)`

`AB=√(20)`

Calculation of BC:

We can use formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

B(0,2) C(3,3)

`BC=√((3-0)^2+(3-2)^2)`

`BC=√(10)`

Calculation of AC:

We can use formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

A(2,6) C(3,3)

`AC=√((3-2)^2+(3-6)^2)`

`AC=√(10)`

Checking right angled triangle:

We can check it by Pythagoras theorem

`AB^2=BC^2+AC^2`

now, we can plug values

`(√(20))^2=(√(10))^2+(√(10))^2`

`20=10+10`

`20=20`

we can see that

left side is equal to right side

so, triangle ABC is right angled triangle.........Answer