<h2>
Answer:</h2>
- The measure of the longest side of ∆ABC is:
b) 6
b) isosceles triangle.
c) right triangle
- The length of side AD is :
b) 5
<h2>
Step-by-step explanation:</h2>
- The vertices of ∆ABC are:
A(1, 7), B(-2, 2), and C(4, 2)
Length of AB is:
Length of BC is:
Length of AC is:
Since, the length of side AC=length of side AB.
Hence, we get:
The triangle is a isosceles triangle.
Also, the longest side of a triangle is: 6 units.
- Now, when a new vertex D(1,2) is added.
then:
Length of AD=
Length BD
and Length AB is:
Also, AD,BD and AB satisfy the Pythagorean Theorem.
Since,
Hence,
∆ABD is a right angled triangle.
and the length of side AD is 5 units