Find the image of (-1, 3) obtained by translating 2 units down, followed by a rotation of 180°
counterclockwise about the origin.
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(1, - 1 )

Step-by-step explanation:

A translation of 2 down means subtract 2 from the y- coordinate

(- 1, 3 ) → (- 1, 3 - 2 ) → (- 1, 1 )

Under a counterclockwise rotation about the origin of 180°

a point (x, y ) → (- x, - y ) , then

(- 1, 1 ) → (1, - 1 )

Overall

(- 1, 3 ) → (- 1, 1 ) → (1, - 1 )

im not sure sorry

Step-by-step explanation:

y - 24 = - 7(x + 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (- 4, 24) and (x₂, y₂ ) = (7, - 53)

m = = = - 7

Using m = - 7 and (a, b) = (- 4, 24 ) , then

y - 24 = - 7(x - (- 4)), that is

y - 24 = - 7(x + 4)