Question 170095: Could someone please help me with this problem? I don't understand. I have to show all work and I don't understand how to do it.
Solve for the following items:
a. The point on the x-axis that is equidistant (equal distance) from (12,6) and (8,2).
b. The distance between the points (6,4) and (18,4).
c. The distance between the points (1,4) and (19,6).
d. The midpoint between (12, 6) and (18, 4)
e. The midpoint between (-6, -8) and (23, 5)
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! Y=mX+b m=SLOPE & b=Y INTERCEPT.
a. The point on the x-axis that is equidistant (equal distance) from (12,6) and (8,2).
slope=(2-6)/(8-12)=-4/-4=1
2=1*8+b
2=8+b
b=2-8
b=-6
Y=X-6
 (graph 300x200 pixels, x from -6 to 8, y from -10 to 10, of TWO functions x -6).
The x axis intercept=6 BUT it is not equal distance from the 2 giv3n points.
To be equal distances between these 2 points it must be between them.
X=6 is not between them.
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b. The distance between the points (6,4) and (18,4).
18-6=12 is the distance between these 2 points.
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c. The distance between the points (1,4) and (19,6).
6-4=2
19-1=18
2^2+18^2=d^2
4+324=d^2
d=sqrt328
d=18.11 is the distance between these 2 points.
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d. The midpoint between (12, 6) and (18, 4)
6-4=2
2/2=1
Y midpoint=6-1=5 or 4+1=5
18-12=6
6/2=3
x midpoint=18-3=15 or 12+3=15
ans. (15, ,5)
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e. The midpoint between (-6, -8) and (23, 5)
5+8=13
13/2=6.5 the Y midpoint.
23+6=29
29/2=14.5 the X midpoint.
ans. (14.5,6.5)
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