Name: Graph of a Linear Equation in R² is a Line
Uploaded: 2019-07-19
Duration: 5 min 50 s
Description: Watch this video and learn more about the graph of a linear equation in R^2, which is a straight line, and also study the conditions required for it.

Question

A triangle has vertices at

(6, 7), (2, - 9)

and

(- 4, 1)

. Find the slope of its medians.

Accepted Answer

Given, a triangle has vertices at $A (6, 7), B (2, - 9)$ and $C (- 4, 1)$ . $D, E$ and $F$ are the points of $A B, B C$ and $C A$ respectively.

Midpoint formula $= (\frac{x_{2} + x_{1}}{2}, \frac{y_{2} + y_{1}}{2})$

Coordinates of the point $D = (\frac{6 + 2}{2}, \frac{7 - 9}{2}) = (\frac{8}{2}, \frac{- 2}{2}) = (4, - 1)$

Coordinates of the point $E = (\frac{- 4 + 2}{2}, \frac{1 - 9}{2}) = (\frac{- 2}{2}, \frac{- 8}{2}) = (- 1, - 4)$

Coordinates of the point $F = (\frac{- 4 + 6}{2}, \frac{7 + 1}{2}) = (\frac{2}{2}, \frac{8}{2}) = (1, 4)$

Slope of a line passing through two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Slope of the median $A E = \frac{- 4 - 7}{- 1 - 6} = \frac{11}{7}$

Slope of the median $B F = \frac{4 - (- 9)}{1 - 2} = \frac{13}{- 1} = - 13$

Slope of the median $C D = \frac{- 1 - 1}{4 - (- 4)} = \frac{- 2}{8} = \frac{- 1}{4}$

Therefore, the slope of the medians of the given triangle are $\frac{11}{7}, - 13$ and $\frac{- 1}{4}$ .

A triangle has vertices at $(6, 7), (2, - 9)$ and $(- 4, 1)$ . Find the slope of its medians.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

A triangle has vertices at 6,7, 2,-9 and -4,1. Find the slope of its medians.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

A triangle has vertices at $(6, 7), (2, - 9)$ and $(- 4, 1)$ . Find the slope of its medians.