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Coordinate Geometry Terms
Coordinate Geometry Definition - It is one of the branches of geometry where the position of a point is defined using coordinates.
What are the Coordinates?
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
Coordinate Plane Meaning - A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
What is the Distance Formula?
It is used to find the distance between two points situated in A(x1,y1) and B(x2,y2)
What is the distance between (4, 0) and (0, 0)?
4
d = (x1 - x2)
= 4 - 0
= 4
What is the distance between (4, 3) and (4, 0)?
3
d = (x1 - x2) + (y1 - y2)
= (4 - 4) + (3 - 0)
= 0 + 3
= 3
What is the distance between (4, 3) and (0, 0)?
Using previous formula, we get
d = (x1 - x2) + (y1 - y2)
= (4 - 0) + (3 - 0)
= 4 + 3
= 7
But we know from
If (x1 - x2) + (y1 - y2) is giving a higher value than what is correct,
What can the distance formula be?
Why not square the x component and square the y component, and then reduce it down by using square root?
(x1−x2)2+(y1−y2)2\sqrt{(x1 - x2)^2 + (y1 - y2)^2}(x1−x2)2+(y1−y2)2
Let’s see if it works…
d=(x1−x2)2+(y1−y2)2d = \sqrt{(x1 - x2)^2 + (y1 - y2)^2} d=(x1−x2)2+(y1−y2)2
=(4−0)2+(3−0)2 = \sqrt{(4 - 0)^2 + (3 - 0)^ 2}=(4−0)2+(3−0)2
=16+9= \sqrt{16 + 9}=16+9
=25= \sqrt{25}=25
=5= 5=5
What is the distance between (2, -1) and (5, 3)?
What is the most logical way to represent a cartesian point in Python?
A. Use two variables, for e.g. x1 and y1 or x2 and y2
B. Use a single tuple variable
C. None of the above
Choice B.
Tuple is the logical way of doing it Python.
What is the for defining a point (3, 4) as a tuple in Python?
A. (3, 4)
B. tuple(3, 4)
C. Both the above are valid
Choice C.
How can you deconstruct a tuple that represents a point?
If
pointA = (6, 8) # construction
then
x1, y1 = pointA # deconstruction
print(x1, y1) # 6, 8
x1, y1, x2, y2 = (1, 2, 3, 4)
What is the value of x1 and y2?
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