Question
Given the 3 Vertices A(3,-1) B(7,-4) C(1,-7) of a triangle, calculate the vector equation and the explicit equation of the height corresponding to side BC
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Answer to a math question Given the 3 Vertices A(3,-1) B(7,-4) C(1,-7) of a triangle, calculate the vector equation and the explicit equation of the height corresponding to side BC
Cristian
4.7119 Answers
To find the vector representing side \overrightarrow{BC}
\overrightarrow{BC} = \begin{pmatrix} 7 \ -2 \end{pmatrix} - \begin{pmatrix} 4 \ 5 \end{pmatrix} = \begin{pmatrix} 3 \ -7 \end{pmatrix}
The normal vector to side BC is \begin{pmatrix} 3 \ -7 \end{pmatrix}
The vector equation of the height from A to BC is given by:
\vec{r}(t) = \begin{pmatrix} 3 \ -1 \end{pmatrix} + t \begin{pmatrix} 3 \ -7 \end{pmatrix}
And the explicit (Cartesian) equation of the height is:
y = -\frac{3}{7}x - \frac{22}{7}
\boxed{y = -\frac{3}{7}x - \frac{22}{7}}
This line passes through point A(3, -1) and is perpendicular to the line segment BC.
The normal vector to side BC is
The vector equation of the height from A to BC is given by:
And the explicit (Cartesian) equation of the height is:
This line passes through point A(3, -1) and is perpendicular to the line segment BC.
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