The distance formula is just the Pythagorean Theorem in disguise.
To calculate the distance AB between point A(x1, y1) and point B(x2, y2), first draw a right triangle which has the segment
as its hypotenuse.
If the lengths of the sides are a and b, then by the Pythagorean Theorem,
(AB)2 = (AC)2 + (BC)2
Solving for the distance AB, we have:
Since AC is a horizontal distance, it is just the difference between the x-coordinates: |(x1 – x2)|. Similarly, BC is the vertical distance |(y1 – y2)|.
Since we're squaring these distances anyway (and squares are always non-negative), we don't need to worry about those absolute value signs.
Find the distance between points A and B in the figure above.
In the above example, we have:
A(x1, y1) = (–1, 0), B(x2, y2) = (2, 7)
Calculate AB to the nearest tenth of a unit.
Determine the distance between the following pair of points to the nearest tenth.
(2, –9), (–3, 3)
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(3, –8), (–2, –5)
(3/4, –7/4), (3/2, 5/4)
(–3, –3), (3, 3)
(5, 0), (3, –2)
(3, 7), (8, –2)
(–4, 9), (–12, 8)
(–3, 9), (–3, –9)
(–5.2, 6.2), (–6.2, 7.2)
Find the distance between the given pair of points. Express your answer in the simplest radical form and in decimal form. If necessary, round your result to the nearest hundredth.
Find the distance between the given pair of points. Express your answer in the simplest radical form and in decimal form. If necessary round your result to the nearest hundredth.
Find the value of a if the distance between the two points is 15 units.
(–6, a), (6, 3)
Find the value of a if the distance between the two points is units.
Find the value of a if the points with the given coordinates are the indicated distance apart.
Plot the points and find the distance.
(3, –3) and (2, 1)
Is the triangle with the vertices T (1, –6), U (1, 3), V (–1, 5) isosceles?
Determine the lengths of the diagonals of the trapezoid with vertices
A(–3, 3), B(12, 8), C(7, 6), D(0, 7) to find if it is isosceles.
Calculate the perimeter of the following figure to the nearest tenth.
The vertices of a parallelogram are (3, 6), (9, 13), (3, –1), and (9, 6).
Sketch the parallelogram, and use the distance formula to verify that opposite sides have equal length.
Sketch the graph of the points (–2, 3), (–2, 5), and (0, 3). Verify whether they form the vertices of a right triangle.
Using the distance formula, obtain the perimeter of the given geometric figure.