Basic geometry: how can you use a translation to find a missing vertex in a rectangle or square? . i know what a translation is, but i don't understand how the sliding of the figure will me to find missing vetex?

A square has all equal sides so say you have 3 points on your graph 2 are below your x-axis and 1 is above your x-axis. If you translate the points below the x-axis to above the x-axis you will fill in you missing point.

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)