Find the length of a line segment, one end of which lies at the origin and the other is a point: a) A (4; 3) b) B (-7; -24)

The length of a segment according to the Pythagorean theorem is calculated as L = √ ((x1 – x2) ² + (y1 – y2) ²), where (x1; y1) are the coordinates of one point of the segment, and (x2; y2) are the coordinates of the second point of the same segment.

In our case, the coordinates of the second point are x2 = 0 and y2 = 0, since by condition one end of the segment lies at the origin.

Numerically, the lengths of the segments are equal:

a) L = √ ((4 – 0) ² + (3 – 0) ²) = √ (16 + 9) = √25 = 5

b) L = √ ((- 7 – 0) ² + (-24 – 0) ²) = √ (49 + 576) = √625 = 25.

Answer: a) 5; b) 25.