the quadrilateral named in parts a through d are parallelograms formed on the diagram at the right.give the coordinates for the fourth vertex.then calculate the slopes of the sides to show that the oppisite sides are parallel. how do you do that
...find the slope? I'm not sure what you don't understand here. I mean, the vertex coordinates are given on the diagram right? Then it's easy. Just find the slope on each side and if the slope on both sides are the same then that proved they're parallel and thus is a parallelogram.
In case you don't know this, for two given coordinates (x1, y1) and (x2, y2), where x and y = any real number. To find the slope:
m = (y2-y1)/(x2-x1)
Note: it doesn't matter which coordinate you set as coordinate 1 or coordinate 2 as long as you are consistent with your selection.
How do you find the measures of an interior angle and an exterior angle of polygons?
To find the coordinates of the fourth vertex of the parallelogram, follow these steps:
1. Identify the coordinates for three of the vertices of the parallelogram. Let's call them A(x1, y1), B(x2, y2), and C(x3, y3). These coordinates should be given in the diagram or in the context of the problem.
2. Compute the difference between the x-coordinates and y-coordinates of points A and B, respectively. This will give you the change in x and y values as you move from A to B.
3. Add the difference to the x-coordinate of point C to find the x-coordinate of the fourth vertex. Similarly, add the difference to the y-coordinate of point C to find the y-coordinate of the fourth vertex. Let's call this new point D(x4, y4).
Now, to calculate the slopes of the sides and demonstrate that opposite sides are parallel, follow these steps:
1. Calculate the slope of one side by using the formula: slope = (change in y)/(change in x). Choose two points that lie on the same side of the parallelogram.
2. Repeat the previous step for the other side of the parallelogram, choosing two points on that side.
3. If the slopes of the two sides are equal, it demonstrates that the sides are parallel.
By following these procedures, you can find the coordinates of the fourth vertex of the parallelogram and calculate the slopes of the sides to show that opposite sides are parallel.