Lydia graphed triangle lmn at the coordinates l (0, 0), m(2, 2) and n(2, -1). she thinks triangle lmn is a right triangle. is lydias assertion correct?

lydias assertion is not correct

Step-by-step 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

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step-by-step explanation: