Question

Use the following information. A trapezoid is isosceles if its two opposite nonparallel sides have the same length. Draw the polygon whose vertices are \(A(1,1), B(5,9), C(2,8),\) and \(D(0,4)\)

Short answer

The plotted points form a quadrilateral polygon. To figure out if it is an isosceles trapezoid, one should calculate the lengths of AD and BC using the distance formula. If the lengths are equal, the polygon is an isosceles trapezoid.

Step-by-step solution

Understand the Coordinate System

A coordinate system can be used to represent points in a plane. The point (x, y) denotes the position x units along the x-axis (horizontally) and y units along the y-axis (vertically). The origin of the coordinate system, represented as (0,0), is the point of intersection of the x and y axes.

Plot the Given Points

To plot these points (A(1,1), B(5,9), C(2,8), D(0,4)) on a coordinate system, you need to move along the x-axis to the value of the first coordinate and then move upwards along the y-axis to the value of the second coordinate. Mark each point on the graph with its respective letter.

Join the Points

After plotting all the points, draw lines to connect the points in order. Start from A (1,1) to B (5,9), then from B to C (2,8), from C to D (0,4). Finally, draw a line back from D to A (1,1) to create a closed figure.

Identify the Polygon

The figure represents a polygon with 4 sides, i.e., a quadrilateral. To determine if it's an isosceles trapezoid, check if two opposite nonparallel sides (i.e., AD and BC) have the same length. Use the distance formula, \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\), to calculate the lengths. If the lengths are equal, the quadrilateral is an isosceles trapezoid.