Area of a Parallelogram - Co-ordinate Geometry
Investigate how to find the area of a parallelogram (with vertex at (0,0)). Click 'Show CD' in order to show the line through C and D, as well as E, its point of intersection with the y-axis. Click 'Show ABFE' (and unclick 'Show ABCD' and 'Show CD') to show the new parallelogram with the vertices A, B, E and new vertex F. Click 'Show Areas' and compare the areas of both parallelograms. Why do you think the areas are like this?# Click 'Show Dimensions' to show the dimensions needed to find the area of parallelogram ABFE.
Once you have investigated the areas of the parallelograms above, take some graph paper and draw a new parallelogram. This time you still need a vertex at (0,0), but instead of numbers for the other vertices, use letters ie. the point B will have coordinates (a,b) and the point C will have coordinates at (c,d). Find the coordinates of D. Hence find the equation of the line CD. Hence find the coordinates of point E. Use the information you have to find the dimensions (base and height) and hence find the area. Now replace (a,b) with () and (c,d) with () You have created a formula for the area of a parallelogram in co-ordinate geometry. Does this look familiar?