Question

Tell whether the lines through the given points are parallel, perpendicular, or neither.

Answer 1

Answer:

The Slope of Line 1 is ->  $-\frac{2}{9}$

The Slope of Line 2 is -> $-\frac{9}{2}$

These two lines are - >  Perpendicular

Step-by-step explanation:

To find the slope of line one, you follow these steps:

First Coordinate 10 -> x1, 5 -> y1

Second Coordinate -8 -> x2, 9 -> y2

Then insert the assigned values into this equation:  $\frac{y2-y1}{x2-x1}$ -> $\frac{9-5}{-8-10}$ which equals $\frac{4}{-18}$ which simplifies to $-\frac{2}{9}$

Then do the same process to find the slop of line 2:

First Coord: 2 -> x1, -4 -> y1

Second Coord: 11 -> x2, -6 -> y2

Then insert the values into this equation: $\frac{y2-y1}{x2-x1}$  ->$\frac{11-2}{-6-(-4)}$ which equals $\frac{9}{-2}$.

We know the lines are perpendicular by:

a. Typing the equations of the lines into a graphing calculator and observing the graph

b. Looking at the slopes. By looking at the slopes, we see that the slope of line 1 is the reciprocal of line 2, and vice versa. Since reciprocal slopes indicate perpendicular lines, the lines 1 and 2 are perpendicular to each other.

Hope this helps!