Question 170095
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( 300, 200, -6, 8, -10, 10, 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.
------------------------------------ 
b. The distance between the points (6,4) and (18,4).
18-6=12 is the distance between these 2 points.
--------------------------------------------
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.
-------------------------------------------------------
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)
----------------------------------------------
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)