To identify the shape, we need to analyze the properties of the lines formed by the given coordinates: A=(5,-2), B=(7,0), C=(1,-2), and D=(-1,0). A key property for quadrilaterals is parallelism of sides, determined by their slopes.
D) Trapezium is the correct answer. A trapezium (or trapezoid) is a quadrilateral with at least one pair of parallel sides. Let's calculate slopes: The line connecting A(5,-2) and C(1,-2) has a slope of ((-2)-(-2))/(1-5) = 0/-4 = 0. The line connecting B(7,0) and D(-1,0) has a slope of (0-0)/(-1-7) = 0/-8 = 0. Since both lines have a slope of 0, they are parallel. The other two sides are not parallel, confirming it's a trapezium.
A) Parallelogram requires two pairs of parallel sides. B) Kite requires two distinct pairs of equal-length adjacent sides. C) Square requires four equal sides and four right angles.