# R, S, and T vertices of a right triangle with a right angle at S HELP PLEASE?

In each of the following R, S, and T are the vertices of a right triangle with the right angle at S.

a: find the slopes of the legs

b. Describe the relationship between these slops. make a mathematical statement describing this relationship.

c: Identify the hypotenuse.

d: Use the pythagroum therom to verify each is a right triangle.

1: R(4,3)

S(2,1)

T(-3,6)

2: R(-1,1)

S(2,4)

T(5,1)

3: R(3,6)

S(5,2)

T(1,0)

4: R(-3,-4)

S(2,-2)

T(14,-8)

Relevance
• 1) 1 , - 1 , √58

2) 1 ; -1 , 4

3) - 2 ; 1/2 ; √40

4) 2 / 5 ; - 1 / 2....not a right triangle as typed

• #1. (a) Slope of RS is 1, slope of ST is -1; (b) slopes are negative reciprocal as expected; (c) the hypotenuse is RT, whose length is sqrt(58); (d) 8 + 50 = 58.

#2. (a) Slope of RS is 1, slope of ST is -1; (b) slopes are negative reciprocal as expected; (c) the hypotenuse is RT, whose length is 6; (d) 18 + 18 = 36.

#3. (a) Slope of RS is -2, slope of ST is +1/2; (b) slopes are negative reciprocals as expected; (c) the hypotenuse is RT, whose length is sqrt(40); (d) 20 + 20 = 40.

#4. your turn to try it