Answer: (x + 6)² + (y + 5)² = 17
Explanation:
1) The equation of a circle is: (x - a)² + (y - b)² = r², wnere:
a is the x-coordinate of the center of the circleb is the y-coordinate of the center of the circler is the radius of the circle
2) Since the points (-7,-1) and (-5,9) define a diameter, you can find the center of the circle as the mid point of the diameter:
x-coordinate of the mid point = (-7 - 5) / 2 = - 12 / 2 = - 6
y-coordinate of the mid point = (-9 - 1)/ 2 = - 10 / 2 = - 5
Therefore, the center of the circle is (-6,-5)
3) The radius of the center is half the diameter.
The length of the diameter is found using the formula for the distance between two points applied to the two endopoints given:
diameter² = (7 - 5)² + (- 1 + 9)² = 2² + 8² = 4 + 64 = 68
⇒diameter = √68 = 2√17
⇒ radius = diamter / 2 = 2√17 / 2 = √17
4) Now you can replace the coordinates of the center and the radius into the equation:
(x + 6)² + (y + 5)² = 17
Y - 9 = 2(x - 1)
This is because the base equation is below:
y - y1 = m(x - x1)
Answer:
Step-by-step explanation:
Step-by-step explanation:
The Pythagorean theorem can be understood as a mathematical relationship between the sides of a right triangle that helps to understand geometric problems in real situations, such as finding measurements, calculating areas, etc.
The theorem says that the square of the hypotenuse is equal to the sum of the squares on the other sides.
In a right triangle the hypotenuse is the longest side of the triangle, on the side opposite to its longest angle, and the other two sides will be the sides. So the Pythagorean theorem formula is:
a² = b² + c²
where a represents the hypotenuse and b and c the other sides.
Answer:

Step-by-step explanation:
