The vertices of ∆PQR are P(–3, 8), Q(–6, –4), and R(1, 1). If you reflect ∆PQR across the x-axis, what will be the coordinates of the vertices of the image ∆P′Q′R′?

P'(–3, -8), Q'(–6, 4),  R'(1, -1).  

Step-by-step explanation:

When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign.

The rule is

(x,y) ⟶ (x,-y)

Thus,

P(-3,8) ⟶ P'(-3, -8)

Q(-6,-4) ⟶ Q'(-6, 4)

R(1,1) ⟶ R'(1, -1)

The coordinates of  the image triangle are:

P'(–3, -8), Q'(–6, 4),  R'(1, -1)

The diagram below shows your source and image triangles. The red and blue arrows show how the points moved during the reflection.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are