Question

State the Midpoint formula?

How are the midpoint formula and the Distance formula alike? How are they different?

Give a real-world example that could be addressed using the distance formula.

Give a real-world example that could be addressed using the midpoint formula.

Answer 1

Let point A (x₁, y₁) and point B (x₂, y₂)

Mid-point formula is given by: $[ \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}]$

The distance formula is given by: $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

The two formula are alike because they both need the information of two coordinate points 

They are different because the mid point formula is adding up then divide by two, whereas the distance formula is subtracting then square the answer.

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Real life problem involving distance formula:

Plane A is spotted on a radar with cartesian coordinate (450, 640).
Plane B is spotted on the same radar with cartesian coordinate (350, 540)

Work out the distance between plane A and plane B.
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Real life problem involving mid point formula

Ms. Holland arranges a treasure hunt for a group of scouts. She marks two points, C and D, with cartesian coordinate (-5, 6) and (7, 10) respectively. The clue is that the treasure is buried in the middle point between C and D. Work out the coordinate where the treasure is buried.