Aims Grade 8 Mathematics Sample Test And Think-Throughs With Answers Page 22
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36December 2009
When I compare the image from the Pythagorean Theorem to the one in the problem, I see that I
am solving for c in my triangle. First, I will find the values for a and b in my image.
(10, 7)
c
a
(2, 1)
b
To find the value of side b of the right triangle, I can take the absolute value of the difference of the
x coordinate of the two vertices, or I can count the squares on the coordinate grid.
b = 2 – 10 = 8 units
To find the value of side a of the right triangle, I can take the absolute value of the difference of the
y coordinate of the two vertices, or I can count the squares on the coordinate grid.
a = 7 – 1 = 6 units
Now I can substitute those values into the Pythagorean Theorem to find c.
a
+ b
= c
2
2
2
6
+ 8
= c
2
2
2
36 + 64 = c
2
100 = c
2
100 = c
2
10 = c
After doing all of the work, I find that c, or the distance between M and N, is 10 units, which is
answer choice D.
Arizona Department of Education
22
Grade 8
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