The vertices of figure KLMN are K(−2, −1), L(−2, −3), M(−5, −3), and N(−5, −1). If figure KLMN is reflected across the line x = 2, find the coordinates of vertex Nˊ.

N'(9, -1)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation include translation, reflection, rotation and dilation.

Reflection is the flipping of an object over the line of reflection. If the point A(x, y) is reflected over the line x = a, the y coordinate would remain but the x coordinate will change.

The vertices of figure KLMN are K(−2, −1), L(−2, −3), M(−5, −3), and N(−5, −1). If figure KLMN is reflected across the line x = 2, the new points would be at:

K'(6, -1), L'(6, -3), M'(9, -3) and N'(9, -1)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.