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

Answer:

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

Step-by-step 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,

$Mid\ point(AB)=(\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2})$

Substituting the values we get

$Q(x,y)=(\dfrac{6+10}{2}, \dfrac{-2+-4}{2})$

$Q(x,y)=(\dfrac{16}{2}, \dfrac{-6}{2})=(8,-3)$

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