On a coordinate plane, a straight line and a parallelogram are shown. The straight line has a positive slope and has a formula of y = x. The parallelogram has points E (3, negative 3), F (5, negative 3), H (2, negative 5), and G (4, negative 5). What are the coordinates of the image of vertex G after a reflection across the line y = x?

(–4, –5)
(4, 5)
(–5, 4)
(5, –4)

Option (3). (-5, 4)

Step-by-step explanation:

Coordinates of the vertices of a parallelogram are,

E(3, -3), F(5, -3), H(2, -5), G(4, -5)

Equation of a line about which this parallelogram was reflected is, y = x

Rule for the reflection will be,

(x, y) → (y, x)

That means when a point (x, y) is reflected across the line y = x, we find a new point (y, x)

By this rule new point by reflecting point G will be,

G(4, -5) → G'(-5, 4)

Therefore, Option (3) will be the answer.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

step-by-step explanation:

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