Question

A line has a slope of -4/5 wich ordered pairs could be points on a line that is a perpendicular to this line?two options (-2,0) and (2,5) (-4,5) and 4,-5) (-3,4) and (2,0)(1,-1) and (6,-5)(2,-1) and (10,9)Please hurry

Answer 1

Step 1

Given;

$\begin{gathered} A\text{ line with a slope of }\frac{-4}{5} \\ m_1=\frac{-4}{5} \end{gathered}$

Required;

$To\text{ find the ordered pairs that could be points on a perpendicular line.}$

Step 2

Write the relationship between the slopes of perpendicular lines and find the slope of the perpendicular line

$\begin{gathered} m_2=-\frac{1_{}}{m_1} \\ m_2\text{ is the slope of the perpendicular line} \\ m_2=-\frac{1}{\frac{-4}{5}} \\ m_2=-1\times(-\frac{5}{4}) \\ m_2=\frac{5}{4} \end{gathered}$

Step 3

Given the points, and applying the formula of the slope can check the points thus

$\begin{gathered} 1)\text{ }\frac{5-0}{2-(-2)}=\frac{5}{4} \\ 2)\frac{-5-5}{4-(-4)}=\frac{-10}{8}=-\frac{5}{4} \\ \end{gathered}$$\begin{gathered} 3)\text{ }\frac{0-4}{2-(-3)}=-\frac{4}{5} \\ 4)\frac{-5-(-1)}{6-1}=\frac{-4}{5} \\ 5)\frac{9-(-1)}{10-2}=\frac{10}{8}=\frac{5}{4} \end{gathered}$

Hence the answer is option 1

written as ( -2,0) and (2,5)

and

Option 5

written as (2,-1) and (10,9)

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