Answer: " (3,1) is the point that is halfway between <em>A</em> and <em>B</em>. " __________________________________________________ Explanation: __________________________________________________ We know that there is a "straight line segment" along the y-axis between "point A" and "point B" ; since, we are given that: ___________________________________________ 1) Points A, B, C, and D form a rectangle; AND:
2) We are given the coordinates for each of the 4 (FOUR points); AND:
3) The coordinates of "Point A" (3,4) and "Point B" (3, -2) ; have the same "x-coordinate" value. ________________________________________________ We are asked to find the point that is "half-way" between A and B. ________________________________________________ We know that the x-coordinate of this "half-way" point is three.
We can look at the "y-coordinates" of BOTH "Point A" and "Point B". ___________________________ which are "4" and "-2", respectively.
Now, let us determine the MAGNITUDE of the number of points along the "y-axis" between "y = 4" and y = -2 .
The answer is: "6" ; since, from y = -2 to 0 , there are 2 points, or 2 "units" from y = -2 to y = 0 ; then, from y = 0 to y = 4, there are 4 points, or 4 "units".
Adding these together, 2 + 4 = 6 units. ______________________________________________ So, the "half-way" point would be 1/2 of 6 units, or 3 units. __________________________________________________ So, from y = -2 to y = 4 ; we could count 3 units between these points, along the "y-axis". Note, we could count "2" units from "y = -2" to "y = 0". Then we could count one more unit, for a total of 3 units; from y = 0 to y = 1; and that would be the answer (y-coordinate of the point). ______________________________________________ Alternately, or to check this answer, we could determine the "halfway" point along the "y-axis" from "y = 4" to "y = -2" ; by counting 3 units along the "y-axis" ; starting starting with "y = 4" ; note: 4 - 3 = 1 ; which is the "y-coordinate" of our answer; that is: "y = 1" ; and the same y-coordinate we have from the previous (aforementioned) method above. ______________________________________________ We know the "x-coordinate" is "3" ; so the answer: _________________________________________________ " (3,1) is the point that is halfway between <em>A</em> and<em> B </em>." __________________________________________________
I'm not sure how to give you solid proof, like an equation or something, but you can see that out of the four coordinates, two of them have the y-value of 4 and two of them have the y-value of 2. Also, there is 1.5 in between each x-value that is paired with the same y-value... if that makes sense. So for (0.5, 2) and (3, 2), there is 1.5 in between 0.5 and 3. I hope this helps! Sorry it's a bit of a weird answer
