Answer:
(3, 1.7)
Step-by-step explanation:
The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.
Two lines are perpendicular if the product of their slopes is -1.
The slope of the line joining D(0,0), F(3,7) is:
The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:
The slope of the line joining E(7,0), and F(3,7). is:
The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:
The point of intersection of equation 1 and equation 2 is the orthocenter. Solving equation 1 and 2 simultaneously gives:
x = 3, y = 1.7
1. 47
2. 70.4 ft per min
3. 13.33333333333333
Answer:
The measure of an interior angle of a regular 15-gon is 120°.
Step-by-step explanation:
We need to determine the measure of the size of an interior angle of a regular 15-gon having 15 sides.
Thus,
The number of sides n = 15
Hence,
Using the formula to determine the measure of an interior angle of a regular 15-gon is given by
(n - 2) × 180° = n × interior angle
substitute n = 15
(15 - 2) × 180 = 15 × interior angle
13 × 180 = 15 × interior angle
Interior angle = (10 × 180) / 15
= 1800 / 15
= 120°
Therefore, the measure of an interior angle of a regular 15-gon is 120°.
Given that the point B is (1,1) is rotate 90° counterclockwise around the origin.
We need to determine the coordinates of the resulting point B'.
<u>Coordinates of the point B':</u>
The general rule to rotate the point 90° counterclockwise around the origin is given by
The new coordinate can be determined by interchanging the coordinates of x and y and changing the sign of y.
Now, we shall determine the coordinates of the point B' by substituting (1,1) in the general rule.
Thus, we have;
Coordinates of B' = 
Thus, the coordinates of the resulting point B' is (-1,1)
