Question

Gio drew an angle on a coordinate grid. One side had the equation `2x-3y=0`, and the other side had the equation `2x+9y=24`. What were the coordinates of the vertex of the angle Gio drew?

Answer 1

The vertex of angle is `(3,2)`.

Explanation:

The coordinates of the vertex is basically the point at which two straight lines indicated by the two equations `2x-3y=0` and `2x+9y=24` intersect.

Coordinates of this point can be found by solving the two simultaneous equations, for which onemay eliminate one variable. For this let ussubtract first equation from second, which gives

`2x+9y-(2x-3y)=24-0`

or `2x+9y-2x+3y=24` or `12y=24` i.e. `y=24/12=2`

Putting this say in first equation we get `2x-3xx2=0` or `2x-6=0`

i.e. `x=6` or `x=3`

Hence point of intersection or the vertex of angle is `(3,2)`

graph{(2x-3y)(2x+9y-24)=0 [-7.5, 12.5, -3.84, 6.16]}