Question

ABC has the points A(1,7) B(-2,2) and C(4,2) as it’s vertices

The measure of the longest side of ABC is _ units. ABC is_triangle. If ABD is formed with the point D(1,2) as it’s third vertex, then ABD is _triangle . The length of side AD is_units

Answer 1

Part 1

Using the distance formula,

`AB=\sqrt{(-2-1)^(2)+(2-7)^(2)}=√(34)\\\\BC=\sqrt{(-2-4)^(2)+(2-2)^(2)}=6\\\\AC=\sqrt{(1-4)^(2)+(7-2)^(2)}=√(34)`

So, the measure of the longest side is 6 units.

Part 2

Triangle ABD will have vertices A(1,7), B(-2, 2), and D(1,2).

We already know that
`AB=√(34)`

Using the distance formula,

`AD=\sqrt{(1-1)^(2)+(7-2)^(2)}=5\\\\BD=\sqrt{(-2-1)^(2)+(2-2)^(2)}=3`

So, ABD is a scalene triangle.

Part 3

From part 2, we know that the length of side AD is 5 units.