50 points! Tell whether the orthocenter is inside, on, or outside the triangle. Then find the coordinates of the orthocenter. Q(-1, 5), R(4, 3), S(-1, -2)

Step-by-step explanation:

Orthocenter is the intersection of altitudes.

We'll calculate the slopes of the two sides and their altitudes ad find the intersection.

Perpendicular slope:

Perpendicular line passes through S(-1, -2):

Perpendicular slope:

Perpendicular line passes through Q(-1, 5):

The intersection of the two lines is the orthocenter.

Solve the system of equations to get the coordinates of the orthocenter:

Find y-coordinate:

The orthocenter is (1, 3)

If we plot the points, we'll see it is inside the triangle

tigers

step-by-step explanation:

cougars 12/10 (12-10 = 2)

bobcats 20/10 (20-10 =10)

bulldogs 8/5 (8-5 =3)

tigers 3/5 (3-5 =-2)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet