Match each type of vector reflection with the matrix used to achieve it

Let us try reflecting (2,3) about x=y and across x-axis and y-axis.

If we are reflecting about y=x, that means both x,y values will be interchanged that is (2,3) will become (3,2)and this will be achieved by .

And for reflection across x-axis,y-value will be multiplied by -1.That is (2,3) becomes (2,-3) and the matrix used to achieve it is .

For reflection across y-axis, x-value will be multiplied by -1. That is (2,3) becomes (-2,3) when reflected across y-axis. The matrix used to achieve it will have -1 in the first place that is

can you add an image ?

step-by-step explanation:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.