Question 818113
For part a:<ol><li>Use the slope formula, {{{m = (y[2]-y[1])/(x[2]-x[1])}}}, to find four slopes:<ul><li>Slope of the line through P and Q</li><li>Slope of the line through Q and R</li><li>Slope of the line through R and S</li><li>Slope of the line through S and P</li></ul></li><li>If the slope through P and Q equals the slope through R and S and the slope through Q and R equals the slope through S and P, then PQRS is a parallelogram. If not, then PQRS is not a parallelogram.</li></ol>For part b:<ol><li>Use the midpoint formula, ({{{(x[1]+x[2])/2}}},{{{(y[1]+y[2])/2}}}) to find four midpoints:<ul><li>The midpoint between P and Q. Name this point A.</li><li>The midpoint between Q and R. Name this point B.</li><li>The midpoint between R and S. Name this point C.</li><li>The midpoint between S and P. Name this point C.</li></ul></li><li>Perform the same steps on ABCD as you did on PQRS in part a: Find four slopes and see if you end up with two pairs of equal slopes. If so, then ABCD is a parallelogram. If not, ABCD is not a parallelogram.</li></ol>