Question: a. plot the points a(-1,-4) and b(-6,2) on the coordinate plane. b. find ab using the distance formula. round to the nearest tenth. c. draw a right triangle with the line ab as the hypotenuse. what is another way you can find ab without the distance formula? d. will this always work? why or why not?

For parts a) and c1), refer to the attached picture.
For part b), the distance formula is:
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Using x1 = -1, y1 = -4, x2 = -6, y2 = 2:
d = sqrt[(-6 + 1)^2 + (2 + 4)^2] = sqrt[25 + 36] = sqrt(61)

Part c2) Another way to find the length of AB without using the distance formula is by drawing the line and measuring it according to the scale.
Part d) This will only work as long as the graph paper is accurately made, and the scale computation is done correctly. However, this will only give approximations, and will not give an exact answer when radicals are involved.

The point (5, 10) will work for the rule y=x+5.y= 10 x= 510=5+510=10therefore the ordered pair (5, 10) works for the rule