Question

Please help me ASAP! Triangle ABC is located at A (2, 3), B (4, 4), and C (6, 3). Zackary says that triangle ABC is an isosceles triangle, while Verna says that it is a right triangle. Who is correct?
Please look at the picture for answer choices thank you

Answer 1

Hello!

The answer is:

The second option,

Zackery, because AB=BC

Why?

To identify which type of triangle is the triangle formed by the given points, first, we need to calculate the distance between the points.

So, finding the distances we have:

From A to B: (2,3) and (4,4)

$distance=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}\\\\distance=\sqrt{(4-2)^{2} +(4-3)^{2}}=\sqrt{2^{2} +1^{2} }=\sqrt{4+1}=\sqrt{5}=2.24units$

From B to C: (4,4) and (6,3)

$distance=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}\\\\distance=\sqrt{(6-4)^{2} +(3-4)^{2}}=\sqrt{2^{2} +(-1)^{2} }=\sqrt{4+1}=\sqrt{5}=2.24units$

Hence, since the distances AB and BC are equal, the triangle is an isosceles triangle, so the answer is:

Zackery, because AB=BC

Have a nice day!