What is true about △abc? check all that apply.

1)ab ⊥ ac
2)the triangle is a right triangle.
3)the triangle is an isosceles triangle.
4)the triangle is an equilateral triangle.
5)bc ∥ ac

Answers and explanation
your answers are:
1) ab ⊥ ac
2) the triangle is a right triangle. 
3) the triangle is an isosceles triangle. 


the distance between points a and b (length of segment ab) can be found using the distance formula (really an application of the pythagorean theorem):

   

the distance between points a and c (length of segment ac) can be found using the distance formula

   

the distance between points b and c (length of segment bc)  can be found by using the distance formula (with the y-coordinate part omitted)

   

to show that this is a right-triangle, we can show that the pythagorean theorem holds for all the triangle lengths:

   

this equation holds true, therefore, " 2)the triangle is a right triangle". bc is the hypotenuse.

" 3)the triangle is an isosceles triangle"  because the length of ab is equal to the length of ac, and they're not equal to the length of bc.

since this is a right triangle,  ∠bac must be a right angle, thus making " 1) ab ⊥ ac" true . this can also be proved using slopes. we use the fact that slope = rise/run.

for ab, the "rise" is +1 and the run is +1 to get to the next "nice" point, therefore the slope of segment ab is +1.

for ac, we have the "rise" +1 but run -1 (in negative direction) to get to the next "nice" point. therefore, the slope of ac is -1.

slopes of ab and ac are negative reciprocals, so ab is perpendicular to ac.

for the other choices:
this is not an equilateral triangle because all the side lengths are not equal.
bc and ac are not parallel lines.

answer:

step-by-step explanation:

from the given figure, ab= (using distance formula)

ab=

also, ac=

ac=

the triangle is an isosceles triangle because the length of ab is equal to the length of ac, and they're not equal to the length of bc.

now, bc=

bc=8

using the pythagoras theorem,

thus,the equation holds. the triangle is a right triangle. bc is the hypotenuse.

since this is a right triangle, ∠bac must be a right angle,thus, ab ⊥ ac.

this is not an equilateral triangle because all the side lengths are not equal.

also, bc and ac are not parallel lines.

hence, option (1), (2) aqnd (3) is correct.

C. i believe it is (5×(-20))+(100×(0.7))