Name: Slope Intercept Form of a Straight Line
Uploaded: 2019-07-19
Duration: 5 min 19 s
Description: There are various forms of equations of a straight line. Watch this video to learn the concept of the slope-intercept form of a line and to draw the graph of...

Question

Find graphically the vertices of the triangle whose sides have the equations

2 y - x = 8, 5 y - x = 14

and

y - 2 x = 1

respectively. Take

1 cm = 1

unit on both the axes.

Accepted Answer

Given:

Let $A B C$ be the required triangle.

Let $A B$ be represented by $2 y - x = 8$ .

$B C$ be represented by $5 y - x = 14$ .

$C A$ be represented by $y - 2 x = 1$ .

For side $A B$

$2 y - x = 8$

$2 y = x + 8$

$y = \frac{x + 8}{2}$

When $x = 0, y = \frac{0 + 8}{2} = 4$

When $x = 2, y = \frac{2 + 8}{2} = 5$

When $x = 4, y = \frac{4 + 8}{2} = 6$

$x$ $y - 2 x = 1$ $2$ $4$

$y$ $4$ $5$ $6$

Then the ordered pairs of the relation $2 y - x = 8$ are, $(0, 4), (2, 5)$ and $(4, 6)$ .

Plotting these points on the same graph paper and drawing a line joining them we obtain the graph of the line represented by the equation $2 y - x = 8$ .

For the side $B C$ .

$5 y - x = 14$

$5 y = x + 14$

$y = \frac{x + 14}{5}$

When $x = 1, y = \frac{1 + 14}{5} = 3$

When $x = 6, y = \frac{6 + 14}{5} = 4$

When $x = 11, y = \frac{11 + 14}{5} = 5$

$x$ $1$ $6$ $11$

$y$ $3$ $4$ $5$

Thus, the ordered pairs of the relation $5 y - x = 14$ are $(1, 3), (6, 4)$ and $(11, 5)$ .

Plotting these points on the same graph paper and drawing a line joining them we obtain the graph of the line represented by the equation $5 y - x = 8$ .

For the side $C A$

$y - 2 x = 1$

$y = 2 x + 1$

When $x = 1, y = 2 (1) + 1 = 3$

When $x = 2, y = 2 (2) + 1 = 5$

When, $x = 3, y = 2 (3) + 1 = 7$

$x$ $1$ $2$ $3$

$y$ $3$ $5$ $7$

Thus the ordered pairs of the relation $y - 2 x = 1$ are $(1, 3), (2, 5)$ and $(3, 7)$ .

Plotting these points on the same graph paper and drawing a line joining them we obtain the graph of the line represented by the equation $y - 2 x = 1$ .

From the graph, we observe that lines $A B$ and $B C$ intersect at $(- 4, 2)$ .

$∴ B \equiv (- 4, 2)$

Lines $B C$ and $C A$ intersect at $(1, 3)$ .

$∴ C \equiv (1, 3)$

Lines $A C$ and $A B$ intersect at $(2, 5)$

$∴ A \equiv (2, 5)$

The coordinates of the vertices of the triangle are $(2, 5), (- 4, 2)$ and $(1, 3)$ .

Find graphically the vertices of the triangle whose sides have the equations $2 y - x = 8, 5 y - x = 14$ and $y - 2 x = 1$ respectively. Take $1 cm = 1$ unit on both the axes.

Important Questions on Coordinates and Solution of Simultaneous Linear Equations Graphically and Distance Formula

Learn and Prepare for any exam you want !

Find graphically the vertices of the triangle whose sides have the equations 2y-x=8, 5y-x=14 and y-2x=1 respectively. Take 1 cm=1 unit on both the axes.

Important Questions on Coordinates and Solution of Simultaneous Linear Equations Graphically and Distance Formula

Learn and Prepare for any exam you want !

Find graphically the vertices of the triangle whose sides have the equations $2 y - x = 8, 5 y - x = 14$ and $y - 2 x = 1$ respectively. Take $1 cm = 1$ unit on both the axes.