Answer:
- (1,3) is inside the triangle
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.
<h3>Side QR</h3>
- m = (3 - 5)/(4 - (-1)) = -2/5
<u>Perpendicular slope:</u>
<u>Perpendicular line passes through S(-1, -2):</u>
- y - (-2) = 5/2(x - (-1)) ⇒ y = 5/2x + 1/2
<h3>Side RS</h3>
- m = (-2 - 3)/(-1 -4) = -5/-5 = 1
<u>Perpendicular slope:</u>
<u>Perpendicular line passes through Q(-1, 5):</u>
- y - 5 = -(x - (-1)) ⇒ y = -x + 4
The intersection of the two lines is the orthocenter.
<u>Solve the system of equations to get the coordinates of the orthocenter:</u>
- 5/2x + 1/2 = x + 4
- 5x + 1 = -2x + 8
- 7x = 7
- x = 1
<u>Find y-coordinate:</u>
The orthocenter is (1, 3)
If we plot the points, we'll see it is inside the triangle
Answer:
yes
Step-by-step explanation:
To determine if the point lies on the line substitute the coordinates into the left side of the equation and if equal to the right side then the point lies on the line
- 3 + (4 × 4) = - 3 + 16 = 13 = right side
Hence (- 3, 4) lies on the line x + 4y = 13
Answer:
depends on the genre.... so sometimes.... Have a good day
Step-by-step explanation: