Question

question 1 (1 point)
suppose you want to create a rectangle using st as one of its sides. what would the slope of the other side through corner s need to be?
image of coordinate grid with points s and t
the slope would need to be: ______
blank 1:

question 2 (1 point)
suppose you want to create a trapezoid using fg as one of its bases. what would the slope of the other base need to be?
image of coordinate grid with points f and g
the slope would need to be: ______
blank 1:
time left for this assessment: 49:52

Explanation:

Question 1

Step1: Find slope of ST

First, identify coordinates of S and T. From graph, S is at (-5, 8), T is at (8, 2). Slope of ST is $m_{ST}=\frac{2 - 8}{8 - (-5)}=\frac{-6}{13}$.

Step2: Determine slope of perpendicular side

In a rectangle, adjacent sides are perpendicular. Slope of perpendicular line is negative reciprocal. So slope of other side through S is $\frac{13}{6}$ (since $m_1\times m_2=-1\implies m_2=\frac{13}{6}$ when $m_1=-\frac{6}{13}$).

Step1: Find slope of FG

Identify coordinates of F and G. From graph, F is at (-5, -1), G is at (4, 4). Slope of FG is $m_{FG}=\frac{4 - (-1)}{4 - (-5)}=\frac{5}{9}$.

Step2: Determine slope of parallel base (trapezoid bases are parallel)

In a trapezoid, the two bases are parallel, so they have the same slope. Thus, the slope of the other base is $\frac{5}{9}$.

Answer:

$\frac{13}{6}$

Question 2