Question

Mark points A (4; −3) and B (−2; 6) on the coordinate plane. Draw AB and find the coordinates of the intersection of the line with the x and y axes.

Answer 1

Intersection points with x and y axis are (2,0) and (0,3) respectively.

Explanation:

Given the two points A(4, −3) and B(−2, 6).

Please refer to the attached image for the graph of line joining the point A and B.

As per graph, the line AB cuts the x and y axis on the points X and Y respectively whose points are X(2,0) and Y(0,3).

Now, let us find the points of intersection of line AB with x and y axis mathematically.

The equation of the line can be given as:

`y = mx+c`

Where (x,y) are the points that lie on the line.

m is the slope and is defined as:

`m = (y_2-y_1)/(x_2-x_1)`

c is the y intercept

Let us calculate Slope of line:

Here,

`x_2 = -2\\x_1 = 4\\y_2 = 6\\y_1 = -3`

`m = (6-(-3))/(-2-4)\\\Rightarrow m =-(9)/(6)\\\Rightarrow m =-(3)/(2)`

So, the equation of line become:

`y=-(3)/(2)x+c`

Putting (x,y) as (4, −3)

`-3=-(3)/(2)* 4+c\\\Rightarrow c = 3`

Rewriting the equation of line:

`y=-(3)/(2)x+3\\\Rightarrow 3x+2y-6=0`

To find intersection point with x axis, let us put y = 0

`3x+2 * 0 -6=0\\\Rightarrow x=2`

Intersection point with x axis is X(2,0)

To find intersection point with x axis, let us put x = 0

`3* 0+2 * -6=0\\\Rightarrow y=3`

Intersection point with x axis is Y(0,3)