Answer :

The length of the segment PQ is 6.32 units

The lengths LM and JK are not the same

The length of a line segment can be calculated using d = √[(x₂ - x₁)² + (y₂ - y₁)²]

For the segment PQ, the endpoints are P(-4, 2) and (2, 0)

Substitute these values into the equation

d = √[(-4 - 2)² + (2 - 0)²]

Evaluate the difference

d = √[(-6)² + 2²]

Evaluate the squares

d = √[36+ 4]

Evaluate the sum

d = √[40]

d = 6.32

For the segment JK, the endpoints are J(-4, 4) and K(-1, 2)

The distance is JK = √[(-4 + 1)² + (4 - 2)²]

JK = √[(-3)² + 2²]

JK = √[9 + 4]

JK = √13

For the segment LM, the endpoints are L(-1, -4) and M(2, -2)

The distance is LM = √[(-1 + 2)² + (-4 + 2)²]

LM = √[1² + (-2)²]

LM = √[1 + 4]

LM = √5

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