Question

calculator
the coordinates of the vertices of △ghj are g(-1,3), h(1,2), and j(-3,-1).
drag and drop the choices into each box to correctly complete the sentences.
the slope of (overline{gh}) is, the slope of (overline{hj}) is
, and the slope of (overline{jg}) is
△ghj a right triangle because

Explanation:

Step1: Calculate the slope of \( \overline{GH} \)

Use the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For \( G(-1,3) \) and \( H(1,2) \), \( m_{GH}=\frac{2 - 3}{1-(-1)}=\frac{-1}{2}=-\frac{1}{2} \)

Step2: Calculate the slope of \( \overline{HJ} \)

For \( H(1,2) \) and \( J(-3,-1) \), \( m_{HJ}=\frac{-1 - 2}{-3 - 1}=\frac{-3}{-4}=\frac{3}{4} \)

Step3: Calculate the slope of \( \overline{JG} \)

For \( J(-3,-1) \) and \( G(-1,3) \), \( m_{JG}=\frac{3-(-1)}{-1-(-3)}=\frac{4}{2} = 2 \)

Step4: Check if it is a right - triangle

We know that if two lines are perpendicular, the product of their slopes is \( - 1 \).
\( m_{GH}\times m_{JG}=-\frac{1}{2}\times2=-1 \)

Answer:

The slope of \( \overline{GH} \) is \( -\frac{1}{2} \), the slope of \( \overline{HJ} \) is \( \frac{3}{4} \), the slope of \( \overline{JG} \) is \( 2 \), \( \triangle GHJ \) is a right triangle because the product of the slopes of \( \overline{GH} \) and \( \overline{JG} \) is \( - 1 \) (they are perpendicular).