Question

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

Answer 1

Part 1

Using the distance formula,

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

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 $AB=\sqrt{34}$

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.