Hanna is plotting a point in coordinate space. She starts at the origin and moves backward eight units along the x-axis. Then she moves right one unit parallel to the y-axis. Finally, she moves down five units parallel to the z-axis and plots the point. What are the coordinates of the point that she plots?

( -8,0, 0) , ( -8, 1, 0) and  ( -8, 1, -5)

Step-by-step explanation:

We need to visualize the given situation in 3D

Coordinates is in the form of (x, y, z)

Henna starts from origin moves back 8 units Negative x-axis

x = -8   point will be ( -8,0, 0)

turning 1 unit right will be parallel to the y axis in positive y-axis direction

y = 1 point will be ( -8, 1, 0)

Moving down by 5 units, Negative z-axis

Z = -5 point will be ( -8, 1, -5)

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.