∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. the measure of the longest side of ∆abc isa)5b)6c)29^(1/2) d.34^(1/2)units. ∆abc is triangle. a. equilateralb)isosceles c. rightd)scaleneif ∆abd is formed with the point d(1, 2) as its third vertex, then ∆abd is trianglea)equilateralb)isosceles c. rightd)scalenethe length of side ad is a.3 b.5 c.8 d.10 units.

                     b)  6

                b)      isosceles  triangle.

                 c)    right triangle

                    b)  5

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.

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

the formula of a midpoint between a abd b: