Question

Classify ΔABC with coordinates A(−3,4), B(−3,−4) and C(1,0).

A) Scalene
B) Equilateral
C) Right Triangle
D) Isosceles

Answer 1

ΔABC with coordinates A(−3,4), B(−3,−4), and C(1,0) is an isosceles triangle because it has two sides of equal length (BC and AC), and one side (AB) of different length.

Step-by-step explanation:

To classify ΔABC with coordinates A(−3,4), B(−3,−4), and C(1,0), we need to calculate the lengths of the sides using the distance formula: √((x2 - x1)2 + (y2 - y1)2). For AB, we use points A and B, for BC, points B and C, and for AC, points A and C.

• Length AB = √((−3 - −3)2 + (4 - (−4))2) = √((0)2 + (8)2) = 8.
• Length BC = √((1 - −3)2 + (0 - (−4))2) = √((4)2 + (4)2) = √(32) = √(16*2) = 4√2.
• Length AC = √((1 - (−3))2 + (0 - 4)2) = √((4)2 + (4)2) = √(32) = √(16*2) = 4√2.

Since two sides (BC and AC) are equal and one side (AB) is different, ΔABC is an isosceles triangle. Therefore, the correct answer is D) Isosceles.