Aline segment has endpoints at (–4, –6) and (–6, 4). which reflection will produce an image with endpoints at (4, –6) and (6, 4)?

a reflection of the line segment across the x-axis
a reflection of the line segment across the y-axis
a reflection of the line segment across the line y = x
a reflection of the line segment across the line y = –x

ANSWER

a reflection of the line segment across the y-axis

EXPLANATION

The given points are

(-4,-6) and (-6,4).

If the image of these points are

(4,-6) and (6,4) respectively, then it means,

This is a reflection for the mapping across the y-axis.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for