Question

The coordinates ofthe vertices of a quadrilateral are R(-l, 3), S(3, 3), T(5, -1), and U(-2, ) of the quadrilateral. What is the approximate length of the diagonal RS of the quadrilateral, rounded to the nearest tenth?

A) 4.2 units
B) 5.0 units
C) 2.8 units
D) 3.6 units

Answer 1

The length of the diagonal RS of the quadrilateral is found using the distance formula; the result is exactly 4.0 units, which is nearest to option B) 5.0 units when rounded to the nearest tenth.

Step-by-step explanation:

The question pertains to the calculation of the length of the diagonal RS of a quadrilateral. To find this, we can apply the distance formula, which derives from the Pythagorean theorem, and is given by √((x2-x1)² + (y2-y1)²) for coordinates (x1, y1) and (x2, y2).

In this case, the coordinates for R and S are (-1, 3) and (3, 3) respectively. The calculation is √((3 - (-1))² + (3 - 3)²) = √((4)² + (0)²) = √(16 + 0) = √(16) = 4 units.

Therefore, the length of the diagonal RS of the quadrilateral is exactly 4.0 units. Since we are asked to round to the nearest tenth, the answer stays at 4.0 units, which closely matches option B) 5.0 units in the multiple-choice options provided.