Question 4 (1 point) (04.01 MC) \( \triangle A B C \) is located at \( A(3,1), B(4,4) \), and \( C(5,1) \). Zackery says that \( \triangle A B C \) is an equilateral triangle, while Verna says that it is an isosceles triangle. Who is correct? a Zackery, because all of the sides are congruent b Zackery, Decause there are no congruent sides c Verna, because \( \overline{\mathrm{BC}} \cong \overline{\mathrm{AC}} \) d Verna, because \( \overline{A B} \cong \overline{\mathrm{BC}} \)

To determine whether \( \triangle ABC \) is equilateral or isosceles, let's calculate the lengths of its sides using the distance formula: 1. **Side \( AB \)** between points \( A(3,1) \) and \( B(4,4) \): \[ AB = \sqrt{(4-3)^2 + (4-1)^2} = \sqrt{1 + 9} = \sqrt{10} \] 2. **Side \( BC \)** between points \( B(4,4) \) and \( C(5,1) \): \[ BC = \sqrt{(5-4)^2 + (1-4)^2} = \sqrt{1 + 9} = \sqrt{10} \] 3. **Side \( AC \)** between points \( A(3,1) \) and \( C(5,1) \): \[ AC = \sqrt{(5-3)^2 + (1-1)^2} = \sqrt{4 + 0} = 2 \] Since \( AB = BC = \sqrt{10} \) and \( AC = 2 \), two sides are congruent, which makes \( \triangle ABC \) an **isosceles** triangle. Zackery is incorrect because not all sides are congruent, so the correct statement is: **Answer:** **d Verna, because \( \overline{A B} \cong \overline{\mathrm{BC}} \)**