To construct parallelogram ABCD in the coordinate grid, one must plot points A and B, calculate the slope between them, find point C using the distance formula to ensure it's 7 units from B, then find point D by ensuring AD and BC are equal and parallel.
To draw parallelogram ABCD with the given conditions, we begin by plotting the given points for A (1,13) and point B (5,8). Since BC is to be 7 units long and lie entirely in the first quadrant, we will use the distance formula to find the coordinates of point C. However, we should also recall that the opposite sides of a parallelogram are equal and parallel to ensure we retain the correct shape.
We can calculate the slope between A and B to determine the direction of side AB, ensuring side CD will have the same slope. Then we find a point C such that the distance from B to C is 7 units and it has the same slope as AB. Subsequently, we can determine the fourth vertex D by ensuring the distances AD and BC are equal, and that the slope of AD is parallel to BC.
Once points C and D are determined, we can draw sides BC and CD using a ruler and protractor, completing the parallelogram ABCD on the coordinate grid. Remember that the parallelogram must have equal opposite sides and both pairs of opposite sides must be parallel to ensure the figure is indeed a parallelogram.