What is the distance between point p and point q? a. half the distance between point a and point k b. twice the distance between point a and point k c. same as the distance between point a and point k

A. half the distance between point A and point K

There are several assumptions we must make in order to answer the question:

Let P' and Q' be points on lines x and y where the line AK intersects those lines, respectively. The distance P'Q' will be the same as the distance PQ. (They are opposite sides of rectangle PP'Q'Q.)

By the nature of reflection, AP' = P'F, and FQ' = Q'K. We know that ...

... AK = AP' +P'F +FQ' +Q'K

By substitution, this becomes ...

... AK = P'F +P'F +FQ' +FQ' = 2P'F +2FQ' = 2(P'F +FQ')

We also know that ...

... P'F +FQ' = P'Q' = PQ

so ...

... AK = 2·PQ

... AK/2 = PQ . . . . . divide by 2

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.