Marguerite drew a rectangle with vertices A (-2,-1) B (-2,-4) and C (1,-4) what are the coordinates of the fourth vortex?

The fourth vortex is (1, - 1)

Concept:

we use the vector method to solve this problem, take all the vertices in vector foam.

In the rectangle their exist two pair of parallel and equal sides, take the one pair and solve for unknown vertex.

BA=CD

A-B = D-C

(-2i-j) - (-2i-4j) = (xi+yj) - (1i-4j)

(-2i-j+2i+4j) = (xi+yj-1i+4j)

3j = xi+yj-1i+4j

i+3j-4j = xi+yj

1i-1j = xi+yj

by comparing,

x = 1

y = - 1

so D vertex is (1, - 1)