Question

Harry plotted a new point Q that partitioned the directed segment from A to B into a 1:1 ratio. A. Find point Q given that A(6, -2) and B (10, -4) B. What is special about point Q? Explain in a complete sentence how you know.

Answer 1

Therefore,

`Q(x,y)=(8,-3)`

As Q is such that Segment AB is partitioned into 1 : 1

1 : 1 means Equally divided in two parts.

∴ Q is the midpoint of AB

Explanation:

Given:

Step-by-step explanation:

Given:

Q is such that Segment AB is partitioned into 1 : 1

Let ,

A(x₁ , y₁) = (6, -2) and

B(x₂ , y₂) = (10, -4)

To Find:

Q( x , y ) = ?

Solution:

As Q is such that Segment AB is partitioned into 1 : 1

1 : 1 means Equally divided in two parts.

∴ Q is the midpoint of AB then By Mid point Formula the Coordinate of Q is given by,

`Mid\ point(AB)=((x_(1)+x_(2) )/(2), (y_(1)+y_(2) )/(2))`

Substituting the values we get

`Q(x,y)=((6+10)/(2), (-2+-4)/(2))`

`Q(x,y)=((16)/(2), (-6)/(2))=(8,-3)`

Therefore,

`Q(x,y)=(8,-3)`

As Q is such that Segment AB is partitioned into 1 : 1

1 : 1 means Equally divided in two parts.

∴ Q is the midpoint of AB