Question

1. what is the slope of the line that is perpendicular to a line that passes through the points a (-2,-3) and b (5, 3)? (g2c) pick the right answer from the possible selections on your screen in eduphoria.
2. find the midpoint of the points a (-2,-3) and b (5, 3). (g2b) midpoint formula: ($\frac{x_1 + x_2}{2}$, $\frac{y_1 + y_2}{2}$) pick the right answer from the possible selections on your screen in eduphoria.
3. what is the distance between points a (-2,-3) and b (5, 3)? (g2b) distance formula: $a^{2}+b^{2}=c^{2}$ or $\sqrt{(x_2 - x_1)^{2}+(y_2 - y_1)^{2}}$ pick the right answer from the possible selections on your screen in eduphoria.
4. which is the inverse of the conditional statement below? if two angles are a linear pair, then they must be supplementary. a. if two angles must be supplementary, then they are a linear pair. b. if two angles are not a linear pair, then they must not be supplementary. c. if two are angles must not be supplementary, then they are not a linear pair. d. two angles are a linear pair, they are supplementary. pick the right answer from the possible selections on your screen in eduphoria.
5. bonus question what is the slope of a line parallel to the graph with equation 2x + 5y = 6? pick the right answer from the possible selections on your screen in eduphoria.

Explanation:

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Step1: Find slope of line through A and B

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-2,-3)$ and $B(5,3)$, we have $m_{AB}=\frac{3-(-3)}{5 - (-2)}=\frac{6}{7}$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_p$. Then $m_{AB}\times m_p=-1$. So $m_p=-\frac{7}{6}$.

Use the mid - point formula $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For points $A(-2,-3)$ and $B(5,3)$, we have $x_1=-2,y_1 = - 3,x_2=5,y_2 = 3$. Then the mid - point is $(\frac{-2 + 5}{2},\frac{-3+3}{2})=(\frac{3}{2},0)$.

Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(-2,-3)$ and $B(5,3)$, we have $x_1=-2,y_1=-3,x_2 = 5,y_2 = 3$. Then $d=\sqrt{(5-(-2))^2+(3-(-3))^2}=\sqrt{(7)^2+(6)^2}=\sqrt{49 + 36}=\sqrt{85}$.

Answer:

$-\frac{7}{6}$

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