What are the coordinates of the image of vertex f after a reflection across the line y=-x ?

answer-

the coordinates of the image of vertex f after a reflection across the line y=-x will be (3, -1)

solution-

the coordinates of the vertices are,

e = (-1, -5)

f = (1, -3)

g = (-2, -3)

h = (2, -5)

while reflecting any point over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).

i.e any point with co-ordinate (x, y), after reflection over y=-x will be (-y, -x)

so, the new coordinates of the vertices will be,

e = (5, 1)

f = (3, -1)

g = (3, 2)

h = (5, -2)

therefore, the coordinates of the image of vertex f after a reflection across the line y=-x will be (3, -1)

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

g

step-by-step explanation: