Question

Graphing equations on a coordinate plane is a simple way to visually represent the relationship between the input values (x) of an equation and the output values (y). This visual representation allows us to make predictions, solve problems, find the point(s) that solve both equations (when there are two), and analyze many other useful business and everyday situations.

Name some real-life situations where graphing could be useful. Discuss your ideas. Name some real-life situations where finding the coordinates of the midpoint of a line segment could be useful.

Choose three non-collinear points on the coordinate plane, making sure none of your points is the origin. On a sheet of paper, graph the three points and draw line segments to connect the points and make a triangle. Label the vertices of the triangle A, B, and C. Now describe the new coordinates of points A, B, and C after the following transformations:

Translation of point A around the origin

90° rotation around point B

Reflection of the triangle across the x-axis

Detail your work and tell what the coordinates of all of the relevant points are.

Choose two coordinate points. On a sheet of paper or in a graphing utility, graph the segment that connects the two points. Now choose a ratio. Divide the segment into two parts according to your ratio. Detail your work and tell what the coordinates of all of the relevant points are.

Choose two different coordinate points. On a sheet of paper or in a graphing utility, graph the line that connects the two points.

Write the equation of this line in slope intercept form. Label it line A.

Now create a new line in slope intercept form that is parallel to line A and that passes through the origin. Label it line B.

Now create a third line in slope intercept form that is perpendicular to line A and passes through the y-intercept of line A. Label it line C.

Answer 1