Question

Three of the vertices of a trapezoid are A(3,-3), B(12, 6) and C(4, 8). The fourth vertex is labeled D. One of its bases is AB. What is the equation of the line that includes base CD?

Answer 1

so hmmm if you notice the picture below, that's the trapezoid

so.... what's really being asked is, "what is the equation of a line that is parallel to AB and passes through 4,8?"

because, a trapezoid bases are the parallel sides, now if AB is one base, CD must be the other parallel one, is the only one across the trapezoid to be parallel with

so, we know the slope if AB is 1, any parallel line to it, has the same slope, so slope of CD is 1

thus $\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 4}}\quad ,&{{ 8}})\quad \end{array} \\\quad \\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 1 \\\\\\ y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-8=1(x-4)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y=x-4+8\implies \boxed{y=x+4}$