Answer:
First box: 4
Second Box: 6
Third Box: 10
Fourth Box: 0
Fifth Box: 4
Sixth Box: -2
Seventh Box: 4
Eighth Box: 0
Ninth Box: 4
[tex]AB = |-2 -(-6)|=4\\AC =|0-(-6)|=6\\AD=|4-(-6)|=10\\BC=|0-(-2)|=2\\BD=|4-(-2)|=6\\CD=|4-0|=4[/tex]
Step-by-step explanation:
Lets go down this question in order from top to bottom.
For question AB we can simply solve the equation given to us with in the brackets.
[tex]AB = |-2 -(-6)|=4[/tex]
First box: 4
For question AC and AD we simply repeat what we did for AB, and simply solve the corresponding equations within the brackets.
[tex]AC =|0-(-6)|=6\\AD=|4-(-6)|=10[/tex]
Second Box: 6
Third Box: 10
Now the fourth box is where we use the first photo.
What this photo is telling us is the location for each of the letters/points.
Point A is at -6
Point B is at -2
Point C is at 0
Point D is at 4
Now lets talk about what the brackets and the answers mean.
The answer you get from the equation that is inside the brackets is the segment length, essentially imagine drawing a straight line that connects every point. The answer is the length of that line.
Sooooo with the first question
[tex]AB = |-2 -(-6)|=4[/tex]
It's asking us for the length of the line segment from point A to point B.
The number 4 is the length of the line segment between the two points.
The numbers inside the bracket's are the locations of the two points.
The rule is put the high number point on the left and subtract the lower number point from it.
In this case point B's value is -2 and point A is -6, so point B goes on the left and you subtract point A from it.
An equation looks like this
Line segment = |(higher value point) - (lower value point)| = length of line segment.
The length of the line segment should always be positive, otherwise it means the the line segment doesn't exist.
Now let's continue with the first box.
[tex]BC=|blank-(-2)|=2[/tex]
Well if we look at our first photo we see that point B is -2 and point C is 0. Meaning that we need to put point C on the left and subtract point B from it.
So lets put point C on the left, we do this by putting a 0 on the left of the -2 because point C is 0.
[tex]BC=|0-(-2)|=2[/tex]
we can even verify this is right by checking the equation with the answer, 0 - (-2) does equal 2, so this is correct.
Fourth Box: 0
Repeat the knowledge we gain and plug in values to the equation
Line segment = |(higher value point) - (lower value point)| = length of line segment.
to get the answers.
Fifth Box: 4
Sixth Box: -2
Seventh Box: 4
Eighth Box: 0
Ninth Box: 4
