Answer:
(-14, 5.5)
Step-by-step explanation:
Perhaps the easiest way to find the 1/4 point is to find (x, y), then find the midpoint between that and M.
(x, y) = 2M -(13, 25) = 2(-5, 12) -(13, 25) = (-23, -1)
Then the 1/4 point is ...
((-23, -1) +M)/2 = ((-23, -1) +(-5, 12))/2 = (-28, 11)/2 = (-14, 5.5)
_____
If we call the end points A(x, y) and B(13, 25), then we know ...
M = (A+B)/2
A = 2M -B . . . . we'll need this in a bit
and the 1/4 point Q is such that ...
(Q -A)/(B -A) = 1/4
4Q -4A = B -A . . . . cross multipliy
Q = (B +3A)/4 = (B +3(2M -B))/4 = (6M -2B)/4 . . . . solve for Q
Q = (3M -B)/2 . . . . reduce the fractions
Q = (3(-5, 12) -(13, 25))/2 = (-28, 11)/2 = (-14, 5.5) . . . as above
Let's start b writing down coordinates of all points:
A(0,0,0)
B(0,5,0)
C(3,5,0)
D(3,0,0)
E(3,0,4)
F(0,0,4)
G(0,5,4)
H(3,5,4)
a.) When we reflect over xz plane x and z coordinates stay same, y coordinate changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.
A(0,0,0)
Reflecting
A(0,0,0)
B(0,5,0)
Reflecting
B(0,-5,0)
C(3,5,0)
Reflecting
C(3,-5,0)
D(3,0,0)
Reflecting
D(3,0,0)
b.)
A(0,0,0)
Moving
A(-2,-3,1)
B(0,-5,0)
Moving
B(-2,-8,1)
C(3,-5,0)
Moving
C(1,-8,1)
D(3,0,0)
Moving
D(1,-3,1)
the equation of a line perpendicular to
and passes through the point (-6,8) is 
Step-by-step explanation:
We need to write equation of line perpendicular to
and passes through the point (-6,8)
Since the line
is in slope-inetercept form 
the slope of line m = 0.25
As, the new line is perpendicular to the given line so, slopes of lines that are perpendicular are: slope = -1/slope1
So, slope will be -1/0.25 = -4
Now, finding y-intercept.

So, value of y-intercept b = 30
Now the equation of the required line having slope m= -4 and b =30 will be:

So, the equation of a line perpendicular to
and passes through the point (-6,8) is 
Keywords: Equation of line, slope-intercept form
Learn more about slope-intercept form at:
#learnwithBrainly