The vertices of a triangle are , , and . What type of triang...

Question Analysis:
This question requires using coordinate - geometry methods to classify a triangle.
The main focus is on calculating side lengths and slopes to determine the triangle's characteristics.

Key Concept Explanation:
An isosceles right - triangle has two sides of equal length and one right angle (two sides with slopes that are negative reciprocals).
The distance formula

is used to find side lengths, and the slope formula

helps identify perpendicular sides.

Step - by - Step Solution:
1. Calculate the lengths of the sides:
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