Question

How would you solve this problem?

Answer 1

Greetings!

To find that these two slopes are the same, you can calculate the gradients of the two lines, which is what all the options are.

The equation for the gradient is:

$\frac{y2 - y1}{x2 - x1}$

Where the differeny y and x values are the two co-ordinates of the lines starting and end point.

Take the line JL, one of the two sets of coordinates are (-4 , 0) and the other set is (-7, 4)

If you use these two sets to substitute into the equation for the gradient, you can use either y coordinates in both sets as y1 or y2 as long as this method is throughout and the x value is the same in both sets ( both numbers are x1 and y1, one cannot be x1 and the other y2).

Lets use ( -4 , 0) and (-7 , 4) which are the coordinates for JL.

y1 = 4 and y2 = 0

0 - 4

Now lets use the two x values:

x1 = -7 and x2 = -4

(-4) - (-7)  

Simply put these two equations in a fraction:

$\frac{0 - 4}{-5 - (-7)}$

Now choose another two sets of values for MP, such as (-10 , 8) and (-1 , -4)

y1 = 8 and y2 = -4

-4 - 8

Lets use the two x values:

x1 = -10 and x2 = -1

-1 - (-10)

Put them into a fraction:

$\frac{-4 - 8}{-1 - (-10)}$

Now these two fractions can be put together, putting an equal sign in middle because they both are same gradient:

$\frac{0 - 4}{-5 - (-7)} = \frac{-4 - 8}{-1 - (-10)}$

Meaning that your answer if G!

Hope this helps!