Question

If a line segment were drawn between points B and C on the graph the midpoint of the segment would be

Answer 1

heya! ^^

the question asks us to find the mid point of the line joining points B and C on the graph.

the coordinates of point B are ( -2 , 3 )

the coordinates of point C are ( 2 , -2 )

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let's start ~

let the coordinates of the midpoint of line segment BC be P ( x , y )

`Applying \: mid \: point \: formula , \\ \\ P(x , y) = ( ( x_(1) + x_(2) )/(2) \: , \: ( y_(1) + y_(2) )/(2) ) \\ \\ P(x , y) = ( ( - 2 + 2)/(2) \: , \: ( 3 + ( - 2))/(2) ) \\ \\ P(x , y) = ( (0)/(2) \: , \: (1)/(2) ) \\ \\ P(x , y) = (0 \: , \: (1)/(2) )`

hence ,

option ( A ) is correct.

hope helpful :D

Answer 2

The midpoint of the line segment BC is A) (0, 1/2).

General Formulas and Concepts:
Algebra I

Coordinate Planes

• Coordinates (x, y)

Midpoint Formula:

`\displaystyle ((x_1 + x_2)/(2),(y_1 + y_2)/(2))`

Explanation:

Step 1: Define

Identify given.

[Graph] Point B(-2, 3)

[Graph] Point C(2, -2)

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint.

1. [Midpoint Formula] Substitute in points B and C:
   
   `\displaystyle ((-2 + 2)/(2),(3 - 2)/(2))`
2. Evaluate:
   
   `\displaystyle (0, (1)/(2))`

∴ we have computed the value of the midpoint to be (0, 1/2).

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Topic: Algebra I