Question

Rectangle pqrs with vertices p(1,2), q(2,5), r(8,3), s(7,0) in the y-axis is a? 1) Square 2) Rectangle 3) Triangle 4) Circle

Answer 1

The figure with vertices P(1,2), Q(2,5), R(8,3), and S(7,0) is a rectangle because the lengths of its opposite sides are equal, suggesting a rectangle rather than other shapes.

Step-by-step explanation:

The question presented asks about the nature of a shape defined by the vertices P(1,2), Q(2,5), R(8,3), and S(7,0). To determine whether it is a square, rectangle, triangle, or circle, we can examine the distances between the vertices. The principle involved is the Pythagorean theorem, stating that in a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

If the coordinates PQ, QR, RS, and SP are equal, we would then classify this as a square. However, in this case, the lengths are not equal and the opposite sides are equal, indicating a rectangle. Therefore, rectangle PQRS with vertices P(1,2), Q(2,5), R(8,3), and S(7,0) is a rectangle.

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