If you have 2 points with the same y coordinates, these 2 points will form a horizontal straight line. For example:

To obtain the distance between two points, subtract the x coordinate of one point off the other, and discard the "-" sign (that is, get the absolute value), if present.

From the graph above, find the distance between points:

(a) A and B

(b) C and D

(c) E and F

(a) Distance of AB = |-4 – 3| = |-7| = 7 units

(b) Distance of CD = |-4 – (-2)| = |-4 + 2| = |-2| = 2 units

(c) Distance of EF = |1 – 4| = |-3| = 3 units

If you're given a graph, the easier alternative is to just count the number of squares sides that the line touches. Multiply that number by the number of units each side represents (in this case, the unit per square is 1).

Calculate the distance between each pair of points given below.

(a) A(4, 3) and B(6, 3)

(b) C(1, -5) and D(-5, -5)

(a) Distance of AB = |4 – 6| = 2 units

(b) Distance of CD = |1 – (-5)| = |1 + 5| = 6 units

To obtain the distance between 2 points, subtract the y coordinate of one point off the other, and discard the "-" sign (that is, get the absolute value), if present.

From the graph above, find the distance between points:

(a) A and B

(b) C and D

(c) E and F

(a) Distance of AB = |-1 – (-4)| = |-1 + 4| = 3 units

(b) Distance of CD = |3 – (-2)| = |3 + 2| = 5 units

(c) Distance of EF = |4 – 2| = 2 units

Calculate the distance between each pair of points given below.

(a) P(-1, -1) and Q(-1, 5)

(b) R(6, -6) and S(6, -2)

(a) Distance of PQ = |-1 – 5| = 6 units

(b) Distance of RS = |-6 – (-2)| = |-6 + 2| = |-4| = 4 units

Pythagoras' theorem states that the square of the hypotenuse (the longest side, c) of a right angled triangle is the sum of the squares of the other 2 sides.

i.e.

So the theorem states that c² = a² + b². You're going to use this knowledge to find the distance between two points on a Cartesian plane.

Say you're given 2 coordinates with different x coordinates and y coordinates respectively. The 2 points can be joined by a line, which can then be imagined to form a right triangle.

Based on the graph above, use Pythagoras theorem to find the distance between point A and B.

Distance of YZ = |2 – 5| = 3 units

Distance of XZ = |3 – (-2)| = 5 units

Using Pythagoras' theorem,

For any 2 points represented by:

In essence, this is Pythagoras' theorem expressed as an algebraic equation. If you use it, you'll find that the steps are identical to using the theorem directly.

Find the distance between the points A(2, -2) and B(-4, -5).

Find the possible values of p if the distance between two points A(1, 2) and B(p, 14) is 13.

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Find the possible values of p of the distance that is a radical?
Damien: What's the full question? Without it, there's an infinite space of solution, …