Question

determine graphically the coordinates of the vertices of the triangle the equations of whose sides are y=x, y=4x,x+y=5. ​

Answer 1

Answer:

y=x and y=4x meets at (0,0)

putting y=x in the equation x+y=5

we get, 2x=5 or, x=5/2

since y=x; y=5/2

therefore, y=x and x+y=5 meets at (5/2,5/2)

Now putting y=4x in the equation x+y=5

we get, 5x=5 or, x=1

since y=4x; y=4×1; y=4

therefore, y=4x and x+y=5 meets at (1,4)

Hence, the coordinates of the vertices of the required triangle is (0,0), (5/2,5/2) and (1,4)

hope it helps...

Answer 2

Concept:

A graph is a representation of the relationship between two or more variables that are measured along one axis of a pair at right angles.

An equation is a formula that uses the equals sign( = ) to connect two expressions to show that they are equal.

Given:

The equations of the sides of a triangle are $y=x,y=4x,x+y=5$.

Find:

The coordinates of the vertices of the triangle.

Solution:

Consider the two equations $y=x$ and $y=4x$ .

These equations will pass through the origin. Therefore, they will meet at $(0,0)$

Substituting $y=x$ in the equation $x+y=5$ ,

$x+y=5\\x+x=5\\2x=5\\x=\frac{5}{2}$

Therefore, $y=\frac{5}{2}$

So, $y=x$ and $x+y=\frac{5}{2}$ intersect each other at $(x,y)=(\frac{5}{2},\frac{5}{2} )$ .

Now,

Consider the two equations $y=4x$ and $x+y=5$.

We have,

$x+y=5\\x+4x=5\\5x=5\\x=1$

and since $y=4x$. Therefore, $y=4$ .

So, the lines $y=4x$ and $x+y=5$ intersect each other at $(1,4)$ .

The coordinates of the vertices of the triangle are $(0,0),(\frac{5}{2},\frac{5}{2}),(1,4)$ .

#SPJ2