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)

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this