Line segment ab below is shown on a coordinate grid: the line segment is rotated 270 degrees counterclockwise about the origin to form a’b’. which statement describes a’b’? a) a’b’ is parallel to ab b) a’b’ is half the length of ab c) a’b’ and ab are equal in length d) a’b’ is greater than twice the length of ab

Only option C is correct, i.e. A’B’ and AB are equal in length.

Step-by-step explanation:

Given is the graph of line AB and it says to rotate it 270 degrees counter-clockwise.

From the graph, the coordinates of A and B are as follows:-

A(1, 3) and B(5, 3)

The rule for 270 degrees counterclockwise rotation is as follows:-

Rotation₂₇₀ (x, y) → (y, -x)

So A(1, 3) → A'(3, -1) and B(5, 3) → B'(3, -5)

Finding slope of AB = (3-3)/(5-1) = 0

Finding slope of A'B' = (-5+1)/(3-3) = ∞

It means AB and A'B' are NOT parallel, but perpendicular lines.

Finding length of AB = (5-1) = 4.

Finding length of A'B' = (-1+5) = 4.

It means Length AB = Length A'B'.

Hence only option C is correct, i.e. A’B’ and AB are equal in length.

b

step-by-step explanation:

given

- 2 (3x + 12y - 5 - 17x - 16y + 4 )

simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the parenthesis by - 2

= 28x + 8y + 2 → b