Question

1. On the graph:a) Draw a scalene right triangle; follow the gridlines to make the right angle. Put all vertices at places where the gridlines intersect.b) Draw a triangle that is not a right traingle. One of the sides needs to be on a gridline, and the vertices need to be on places where the gridlines intersect.c) Draw two circles of different sizes. Use a compass if possible. Make it easy to determine the length of the radii. Mark the center of each circle.d) Draw a parallelogram that is not a square or rectangle with two of the parallel sides on gridlines.e) Draw a trapezoid with the parallel sides on gridlines. 2. Neatly color every other column on your graph paper one color, but do not color inside the shapes. You can use markers, colored pencils, or crayons. After that, color every other column inside your shapes with the same color, coloring the opposite columns that you colored outside the shapes.3. Answer the questions:a) What is the area of each triangle? Right triangle: ____ Other triangle: ______b) What is the exact length of one of the sides of the triangle from 1b that is not on a gridline? _____c) Label one acute angle of your right triangle B. What is sin B? ____ What is cos B? ____ What is tan B? ____d) What is the scale factor for the circles? ___e) Write the translation rule for the circles: (x, y) -> (___,___)f) What is the exact circumference of the smaller circle? _____g) What is the approximate area of the larger circle? Use 3.141 for pi and round your answer to the nearest hundredth. ____h) What is the area of the parallelogram?i) What is the perimeter of the parallelogram?j) What is the area of the trapezoid?k) What is the perimeter of the trapezoid?(This is one whole big question.)

Answer 1

We are given the picture of a cartesian plane. Notice that the darker lines are the coordinate axis and the light gray lines are the gridlines.

We begin by drawing a line on one of the gridlines. This would be the side that is on the gridlines. For example,

WE are told that the triangle can't be a right triangle. Recall that right triangles look as follows

They are characterized by having one of the angles to have a measure of 90°.

So, to avoid this, we pick a point that is not located on the horizontal lines of boths ends of the red line. For example

Finally, we join this point with both ends of the red line. So we get

From our construction, this triangle fulfills all the requirements.