Which of the following statements are true? select all that apply. a) the image of the point (-3,-5) under a reflection across the x-axis is (3,-5). b) the image of the point (1,9) under a reflection across the y-axis is (1,-9). c) the image of the point (8,7) under a reflection across the line y=-x is (-7,-8). d) the image of the point (-6,-6) under a reflection across the y=x is (-6,-6). e) the image of the point (2,4) under a reflection across the y-axis followed by a reflection across y=xis (-2,-2). f) point k (3,-1)is reflected across the x-axis to creak point k'.the line x+3y=6 passes through point k'.

The answer in order are false, false, true, true, false and (3,1)

Step-by-step explanation:

We know that image of a point (x,y) under the y-axis

is (-x,y) i.e. the sign of x coordinate changes

Similarly in case of x-axis sign of y coordinate changes

i.e (x,y) is reflected to (x,-y)

Also the reflection of (x,y) under the line y=x is (y,x)

and the reflection of (x,y) under the line y=-x is(-y,-x)

So  

a) Given image of (-3,-5) under x-axis is (3,-5).

Hence statement is false

b) Given image of (1,9) under y-axis is (1,-9)

Hence the statement is false

c) Given image of (8,7) under y=-x is (-7,-8)

i.e. the statement is true

d) Given image of (-6,-6) under y=x is (-6,-6)

i.e the statement is true

e) Given image of (2,4) under y axis followed by x-axis is (-2,-2)

Hence the statement is false

f) (3,-1) is reflected in x-axis to (3,1)

Hence the point k is (3,1)

yes

step-by-step explanation: