In right triangle abc, c is the right angle. If the coordinates of A are (-1,1) and the coordinates of B are (4,-2). the coordinates of c maybe?
All we have is the hypotenuse AB.
Any point C on a circle with AB as a diameter will have a right angle at C.
So, unless they have given you choices, or otherwise placed conditions on C, it's pretty open-ended.
Since the center of the circle is (3/2,-1/2), and the radius of the circle is √34, the equation of the circle is
(2x-3)^2 + (2y+1)^2 = 34
Naturally, if the triangle has legs parallel to the axes, then obvious choices for C are (4,1) and (-1,-2).
Oops. The diameter is √34, not the radius.
Well, it looks like we have a right triangle on our hands! So, to find the coordinates of point C, we can utilize the Pythagorean theorem.
The distance between points A and B can be found using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Applying this formula to points A and B, we get:
dAB = sqrt((4 - (-1))^2 + (-2 - 1)^2)
= sqrt(5^2 + (-3)^2)
= sqrt(25 + 9)
= sqrt(34)
Now, since C is the right angle and it's the farthest point from A, the distance from C to A would also be dAB. Therefore, the coordinates of C would be located at the endpoint of a line segment with length sqrt(34) and direction opposite to the line segment AB.
However, with only the information given about points A and B, we cannot determine the exact coordinates of C. So, I guess point C is at a secret location. Maybe it's off enjoying a vacation on a tropical island! 🏝️🌴
To find the coordinates of point C in a right triangle, we can use the midpoint formula. The midpoint of the hypotenuse AB will give us the coordinates of point C.
Step 1: Find the midpoint of AB:
The midpoint is found by averaging the x-coordinates and the y-coordinates of A and B.
Midpoint_x = (x-coordinate of A + x-coordinate of B) / 2
= (-1 + 4) / 2
= 3 / 2
= 1.5
Midpoint_y = (y-coordinate of A + y-coordinate of B) / 2
= (1 + (-2)) / 2
= -1 / 2
= -0.5
So, the midpoint of AB is (1.5, -0.5).
Step 2: The midpoint of AB is also the coordinates of C, since C is the midpoint of AB in a right triangle.
Therefore, the coordinates of C are (1.5, -0.5).
To find the coordinates of point C in the right triangle ABC, where point C is the right angle (90-degree angle or the hypotenuse), you can use the midpoint formula.
Given that A has coordinates (-1, 1) and B has coordinates (4, -2), the midpoint between these two points will be the coordinates for point C.
The midpoint formula is as follows:
Midpoint (x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's apply the formula to find the coordinates of point C:
Midpoint (x, y) = ((-1 + 4) / 2, (1 - 2) / 2)
= (3 / 2, -1 / 2)
Therefore, the coordinates of point C are (3/2, -1/2).