Question

Are the lines created using the given points perpendicular?L1: (1,2), ( 3,1) and L2: (0,-1), (2,0)

Answer 1

`No,\text{ they are not}`

Step-by-step explanation:

To check for this, we have to get the slope of the two lines

The slope of a line can be calculated using the formula:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

where (x1,y1) are the coordinates of the first point and (x2,y2) are the coordinates of the second

Mathematically, we have the slope of the first as follows:

`m\text{ = }(1-2)/(3-1)\text{ = -}(1)/(2)`

For the second line, we have it that:

`m\text{ = }(0+1)/(2-0)\text{ = }(1)/(2)`

When two lines are perpendicular, the product of their slopes is equal to -1

We have it that:

`(1)/(2)*(-(1)/(2))\text{ = -}(1)/(4)`

This shows that the two lines are not perpendicular