PRACTICE: Finding distance on the coordinate plane
LEVEL 2
1) a. What’s the distance between points A and B?
b. Is that the same as the distance between B and A?
2) a. What’s the distance between points C and B?
b. How could you write that distance as an absolute value expression?
3) What’s the distance between points D and A? Find an exact answer.
4) What’s the distance between points E and C? Express your answer as an exact
simplified root, not a decimal approximation.
5) SUPER CHALLENGE: ADC sort of looks like a right angle, but is it? How could
you prove whether or not it is?
D. Stark 2/28/2017
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PRACTICE: Finding distance on the coordinate plane
KEY
LEVEL 2
1) a. What’s the distance between points A and B? 3 units
b. Is that the same as the distance between B and A? Yes.
Distance is always positive. It doesn’t matter which point you start from.
2) a. What’s the distance between points C and B? 6 units
b. How could you write that distance as an absolute value expression?
| –9 – (–3) |
(That simplifies to | –9 + 3 | = | –6 | = 6 )
Distance is the absolute value of the difference. (Notice that it doesn’t matter
which value you put first. The absolute value symbol will make the final result
positive.)
D. Stark 2/28/2017
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3) What’s the distance between points D and A? 5 units
Notice that  DBA is a right triangle with legs of 3 and 4 units. You might spot
right off that this is a Pythagorean Triple, a 3-4-5 triangle, which is a useful
thing to memorize. (Any scaling up of a 3-4-5 triangle is also a right triangle;
for example, a 6-8-10 triangle).
If you don’t spot that, you can use the Pythagorean Theorem to calculate the
missing length. The theorem is on your formula sheet.
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
C=
√𝟐𝟓 = 5
4) What’s the distance between points E and C? Express your answer as a
simplified root, not a decimal approximation.
This is another Pythagorean Theorem problem.
a2 + b2 = c2
22 + 62 = c2
4 + 36 = c2
40 = c2
c = √𝟒𝟎 = √𝟒
• 𝟏𝟎 = √𝟒 • √𝟏𝟎 = 𝟐√𝟏𝟎
D. Stark 2/28/2017
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5) SUPER CHALLENGE: ADC sort of looks like a right angle, but is it? How could
you prove whether or not it is?
If ADC were a right angle, then the Pythagorean Theorem would hold for
 ADC. But if the theorem doesn’t hold true here, then it’s not a right angle.
We found above that DA = 5
We can count that AC = 9
We can use the Pythagorean Theorem with DBC to find that DC = √𝟓𝟐
DB = 4
CB = 6
a2 + b2 = c2
42 + 62 = c2
16 + 36 = c2
52 = c2
c = √𝟓𝟐
Now the question is: does the Pythagorean Theorem hold for  ADC?
Let’s see…
52 + (√𝟓𝟐)2 = 92
25 + 52 = 81
77  81
No, the Pythagorean Theorem doesn’t hold here, so it isn’t a right angle. The
Pythagorean Theorem works on all right triangles and only right triangles.
D. Stark 2/28/2017
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