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On the Cartesian plane, the midpoint between two points $A(a,b)$ and $B(c,d)$ is $M(m,n)$. If $A$ is moved vertically upwards 20 units and horizontally to the right 14 units, and $B$ is moved vertically downwards 4 units and horizontally to the left 2 units, then the new midpoint between $A$ and $B$ is $M'$. What is the distance between $M$ and $M'$

Answer :

The distance between M and M' is 10 units.

What is a cartesian plane?

  • Cartesian Plane is a two-dimensional plane in the cartesian coordinate system.
  • Rene Descartes designed the cartesian plane in the 17th century.
  • The most important property of a cartesian plane is that it connects two branches of mathematics: Euclidean Geometry and Algebra.

To find the distance between M and M', calculate as follows:

Let,

[tex]M=[\frac{(a+c)}{2},\frac{(b+d)}{2} ]=(m,n)\\A'=(a+14,b+20); B' =(c-2,d-4)\\M'=[\frac{(a+c)+12}{2},\frac{(b+d)+16}{2}=(m+6,n+8)\\\sqrt{[(m+6-m)^{2} +(n=8-n)^{2} } =\sqrt{[6^{2} +8^{2} ]} =\sqrt{36+64} =\sqrt[]{100}\\\sqrt[]{100} =10[/tex]

Therefore, the distance between M and M' is 10 units.

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