Question

∆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 is
a)5
b)6
c)29^(1/2)
d)34^(1/2)
units. ∆ABC is triangle.
a)equilateral
b)isosceles
c)right
d)scalene

If ∆ABD is formed with the point D(1, 2) as its third vertex, then ∆ABD is triangle
a)equilateral
b)isosceles
c)right
d)scalene
The length of side AD is
a)3
b)5
c)8
d)10 units.

Answer 1

First, we need to remember that the distance between two points (x1, y1) and (x2, y2) can be calculated with √[ (x1 - x2)^2 + (y1 - y2)^2 ]. Thus, we apply this formula to measure the lengths of AB, BC, and AC in ∆ABC. AB = √[ (1 - -2)^2 + (7 - 2)^2 ] = √25 = 5 units BC = √[ (-2 - 4)^2 + (2 - 2)^2 ] = √36 = 6 units CA = √[ (4 - 1)^2 + (2 - 7)^2 ] = √25 = 5 units From this, we can clearly see that BC is the longest side of ∆ABC with a length of √36 = 6 units. Thus, the answer is B: 6. Since ∆ABC sides 5, 5, and 6. That makes it an isosceles triangle. Which makes the right answer to be B: isosceles. Now, if we form a new triangle, ∆ABD, with D at (1, 2), we have the following lengths: AB = 5 units BD = √[ (-2 - 1)^2 + (2 - 2)^2 ] = √9 = 3 units AD = √[ (1 - 1)^2 + (7 - 2)^2 ] = √25 = 5 units Similarly, since ∆ABD has sides with lengths of 5, 3, and 5. This means it is isosceles. The answer for this item is B: isosceles. We have shown above that AD is 5 units. Thus, answer is B: 5.

Answer 2

BC is the longest side of ∆ABC with a length of 6 units.

The lengths makes it an isosceles triangle.

The new triangle is a Right Scalene

AD is 5 Units

Explanation:

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