Answer:
lydias assertion is not correct
Explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
It is given that, triangle LMN at the coordinates L (0, 0), M(2, 2) and N(2, -1).
To find the side lengths of triangle LMN
By using distance formula,
LM = √[(2 - 0)² + (2 - 0)²]
=√[4 + 4]
= √8
MN = √[(2 - 2)² + (-1 - 2)²]
=√[0 + 9]
= √9 = 3
LN = √[(2 - 0)² + (-1 - 0)²]
=√[4 + 1]
= √5
To check ΔLMN is right triangle
LN < LM <MN
LN² + LM² = (√5)² + (√8)² = 13
MN² = 3² = 9
Therefore LN² + LM² ≠ MN²
lydias assertion is not correct