Δzap has coordinates z (−1, 5), a (1, 3), and p (−2, 4). a translation maps point z to z' (1, 1). find the coordinates of a' and p' under this translation.

To solve this problem, we should first identify the number of units that point Z was translated. The number of units of movement of point Z should be similar to the number of units of movement of points A and P.

Let us say that the movement is Δx and Δy for horizontal and vertical translations respectively.

From Z to Z’:

Δx = 1 – (-1) = 2

Δy = 1 - 5 =  - 4

Therefore the translation is in the form of (x + 2 , y – 4). Points A and P then becomes:

A’ = (1 + 2 , 3 – 4)

A’ = (3, -1)

P’ = (-2 + 2, 4 – 4)

P’ = (0, 0)

Answers:

A’ = (3, -1)

P’ = (0, 0)

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

23

step-by-step explanation: