Question

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Answer 1

Step 1: State the given coordinates in the question

`\begin{gathered} A(x_1,y_1) \\ B(x_2,y_2) \\ C(x_3,y_3) \\ D(x_4,y_4) \end{gathered}`

Step 2: Find the slope of Line segment AB

`\begin{gathered} \text{let slope of line segment AB be m1} \\ m_1=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Step 3: Find the slope of the line segment CD

`\begin{gathered} \text{let slope of line segment CD be m2} \\ m_2=(y_4-y_3)/(x_4-x_3) \end{gathered}`

Step 4: State the condition for which line AB and line CD are perpendicular to each other

The condition for which two lines are perpendicular to each other is that the slope of one of the lines is equal to the negative inverse of the other line. This can be represented mathematically by applying it the line AB and line CD

`\begin{gathered} m_1=(-1)/(m_2) \\ m_1m_2=-1 \end{gathered}`
`_{}(y_2-y_1)/(x_2-x_1)*(y_4-y_3)/(x_4-x_3)=-1`

Hence, the correct option is OPTION C