Find the length of the smaller of the diagonals of the parallelogram whose vertices have coordinates (1; 4), (5; 4), (6; 8), (2; 8).

We have 4 points, check if the quadrangle, the vertices of which are the points, is a parallelogram.

A (1; 4), B (5; 4), C (6; 8), D (2; 8).

| AB | = ((5 – 1) ^ 2 + 0) ^ (1/2) = 4;

| BC | = ((6 – 5) ^ 2 + (8 – 4) ^ 2) ^ (1/2) = (1 + 16) ^ (1/2) = 17 ^ (1/2);

| CD | = ((2 – 6) ^ 2 + 0) ^ (1/2) = 4;

| AD | = ((2 – 1) ^ 2 + (8 – 4) ^ 2) ^ (1/2) = (1 + 16) ^ (1/2) = 17 ^ (1/2).

Opposite sides are equal, ABCD is a parallelogram.

Find the diagonals:

| AC | = ((6 – 1) ^ 2 + (8 – 4) ^ 2) ^ (1/2) = (25 + 16) ^ (1/2) = 41 ^ (1/2);

| BD | = ((2 – 5) ^ 2 + (8 – 4) ^ 2) ^ (1/2) = (9 + 16) ^ (1/2) = 5 is the smallest diagonal.