Geometry
Unit 1 – 1.3
Distance and Midpoint Formula
NAME _________________________________________________ DATE __________________________
Apply your knowledge of the distance formula, midpoint formula, Pythagorean theorem, and
writing equations of lines below to complete the worksheet.
Distance formula: d =
( x2 - x1 )2 + ( y2 - y1 )2
æx +x y +y ö
Midpoint Formula: M = ç 1 2 , 1 2 ÷
è 2
2 ø
Pythagorean Theorem: a 2 + b 2 = c2
1.) What is the perimeter of the triangle? Explain the steps you used to find your answer.
Steps and answer below:
2.) Find the perimeter of the triangle:
3.) Plot the points A(5, -4) and B(-2, 6) on the coordinate plane below. Find the midpoint C of the two points using
the midpoint formula. Then prove that this is the answer by using the distance formula. In other words, since a
‘midpoint’ is suppose to be in the middle, shouldn’t the length of AC and CB be equal?
Geometry
Unit 1 – 1.3
Distance and Midpoint Formula
4.) Find the midpoint of each of the sides of triangle ABC and label the new points D, E, and F.
Then connect the points to form a smaller triangle DEF. What is the perimeter of △ DEF?
Also answer the questions.
a.) What two formulas will you use?
b.) What will you use each formula for?
5.) Is △ ABC a right triangle? Prove that your answer is correct by using slope. Explain the
steps you took to prove your answer below.
6.) Let’s pretend that you have forgotten how to use slopes to prove if the triangle is a right
triangle. Is there another way to show this? What steps and formulas are involved?
Show the work below to prove your answer a way other than slopes.
7.) Write the equation of lines formed by AB, BC, and AC in △ABC
Geometry
Unit 1 – 1.3
Distance and Midpoint Formula
Extra practice:
8.) a.) Find the perimeter of the triangle. _______________
b.) Is the triangle a right triangle? ________________
You must justify your answer through slope, distance formula, and/or Pythagorean
theorem.
c.) Find the midpoint of each of the sides of the triangle. Label the points on the graph.
9.) a.) Find the perimeter of the triangle. _______________
b.) Is the triangle a right triangle? ________________
You must justify your answer through slope, distance formula, and/or Pythagorean
theorem.
d.) Find the midpoint of each of the sides of the triangle. Label the points on the graph.