Look at the data below from two random samples of a 100 students favorite lunch food from two different schools. which of the fo
llowing inferences can be made from the data above?
A. Students at Grant Middle School don't eat lunch
B. Above the same amount of pizza will be sold at both schools
C. More Students at Jackson Middle School prefer cheeseburgers
D. Students at Grant Middle School are three times more likely to purchase salad than Jackson Middle School.
A. Students at Grant Middle School don't eat lunch
B. Above the same amount of pizza will be sold at both schools
C. More Students at Jackson Middle School prefer cheeseburgers
D. Students at Grant Middle School are three times more likely to purchase salad than Jackson Middle School.
1 answer:
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<h3>Answer: (2, 3)</h3>
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Explanation:
For now, we're only going to consider Newmarket and Markham, which are points N and M respectively.
Let's find the slope of line NM through use of the slope formula.
m = (y2-y1)/(x2-x1)
m = (3-8)/(7-2)
m = -5/5
m = -1
Line NM has a slope of -1. Its perpendicular slope is +1 or just 1.
Rule: If the slopes multiply to -1, then the lines are perpendicular.
Or you can apply the negative reciprocal rule to go from -1 to 1.
We'll keep this perpendicular slope in mind for later.
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Now let's find the midpoint of points N and M.
Add up the x coordinates and divide by 2: (x1+x2)/2 = (2+7)/2 = 4.5
Do the same for the y coordinates: (y1+y2)/2 = (8+3)/2 = 5.5
The midpoint of N and M is at (4.5, 5.5)
The perpendicular line must go through these two points. I'm going to skip a few steps here, but basically we go from y = mx+b to y = x+1 after plugging in those x,y values and the perpendicular m we found earlier.
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In short, the perpendicular bisector for line segment NM is the equation y = x+1.
If you follow the same steps as the previous two sections, but you apply them for points M and V instead, then you should find that the perpendicular bisector is y = -3x+9. I'm skipping steps here as well.
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At this point, we have the system of equations
Let's use substitution to solve for x and y
y = x+1
-3x+9 = x+1
-3x-x = 1-9
-4x = -8
x = -8/(-4)
x = 2
y = x+1
y = 2+1
y = 3
So together, x = 2 and y = 3 pair up to get the ordered pair solution (x,y) = (2,3)
This is the location where the theme park should be placed. Let's say that C = (2,3). I'm using C for center.
You can use the distance formula to confirm that segments CN, CM and CV are all the same length, which would verify that point C is equidistant from all the other points. Furthermore, it means that points N, M and V are all on the same circle centered at C.
I know it says not to use a graph, but it still helps to see what's going on. Also, it's a handy way to confirm the answer. I used GeoGebra to make the graph. See the diagram below.
Side note: you only need 2 perpendicular bisectors to find point C. You could use three, but that's overkill since they all intersect at the same location.