Aline segment with endpoints a(-4, 3, 2) and b(5, -6, -1) is translated first two units back and 3 units right and 1 unit up the image is then translated 7 units to the left
what are the coordinates of b
a. (3, 4, 0)
b. (3, -10, 0)
c. (5, -6, -1)
d. (-4, -10, -7)

Option B. (3,-10,0) is the right answer.

Step-by-step explanation:

In these questions we should always remember x-axis represents a line in front of us, y-axis represents a line horizontally perpendicular to the line representing x-axis and Z- axis is vertically perpendicular to the x and y- axis.

So shifting front or back means it's a change on x- axis coordinates, shifting right or left means translated on y-axis and moving up and down means translated on z- axis.

Now point for B(5, -6, -1)  

x- axis -- 5 - 2 (shifted 2 units back means moved back on x-axis)

y- axis -- (-6) + 3 (shifted 3 units right means right movement on y-axis)

z-axis -- (-1) + 1 ( shifted 1 unit up means increase in z coordinate)

So the new endpoint will be B'(2, -3, 0)

Now as per question image is further translated 7 units left that means

y-axis -- -3 + (-7) (shifted 7 to the left on y axis)

Therefore new end point will be (3, -10, 0).