SME
Grade 8 Math · Problem type
Distance between two points
Use this for “Find the distance between (−9, −12) and (0, 0)” or “How long is the segment on the grid?”
Chart
From (−4, −2) to (4, 4): legs 8 across and 6 up.
d² = 8² + 6² = 64 + 36 = 100
d = √100 = 10 units
This is an example. Type your own values to start a new problem.
d
=
(
−
(
)
)
2
+
(
−
(
)
)
2
Formulas
d
=
√(
(
x₂
−
x₁
)
2
+
(
y₂
−
y₁
)
2
)
(distance
=
√((second
x
−
first
x)²
+
(second
y
−
first
y)²))
10 = √((4 − (−4))² + (4 − (−2))²)
Assumptions
•
The distance between two points is the hypotenuse of a right triangle.
•
Its legs go straight across and straight up, along the grid lines.
•
Count each leg on the grid, or subtract the coordinates.
Step-by-step
WE KNOW
x₁ = −4 (first x), y₁ = −2 (first y), x₂ = 4 (second x), y₂ = 4 (second y)
FIND
distance (d)
Step 1 · Find distance (d)
Use d = √((x₂ − x₁)² + (y₂ − y₁)²) (distance = √((second x − first x)² + (second y − first y)²))
The legs are the change in x and the change in y. Square, add, take the root.
d
=
√((4
−
(−4))²
+
(4
−
(−2))²)
Across: 4 − (−4) = 8
Up: 4 − (−2) = 6
d
=
√
8
2
+
6
2
=
√
64 + 36
d
=
√
100
d
=
10
Check
Put the numbers back in. Both sides should match.
10 = √((4 − (−4))² + (4 − (−2))²) ✓
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Pythagorean theorem and distance between points
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A diagonal through a box
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Related lessons
Pythagorean theorem and distance between points
Main lesson
A diagonal through a box
Use this for “Will a 30 cm umbrella fit flat in a 20 cm by 15 cm by 18 cm box, corner to corner?”
Is it a right triangle?
Use this for “Which of these could be the sides of a right triangle?” with the converse of the Pythagorean theorem.