Lucinda is writing a coordinate proof to show that a diagonal of a parallelogram partitions the parallelogram into two equal areas.

Enter your answers in the boxes to complete Lucinda's proof.

Since KLMN is a parallelogram and a parallelogram's opposite sides are parallel and congruent, the coordinates for M are (4x,__).

In △KMN, the length of the base is ___ and the height is ___. So an expression for the area of △KMN is ___.

In △KLM, the length of the base is 3x and the height is 2y. So an expression for the area of △KLM is ___.

Comparing the area of the two triangles that are formed by a diagonal of the parallelogram shows that a diagonal of a parallelogram partitions the parallelogram into two equal areas.

What signals you that factoring by grouping is the best method to use when factoring a problem?

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Which of the following equations is of the parabola whose vertex is at (4, 3), axis of symmetry parallel to the y-axis and focus at (4, -3)? a.) y+3=1/24 (x+4)^2 b.)y-3=-1/24 (x-4)^2 c.)x-4=-1/24 (y-3)^2