Assume triangle JKL is in the first quadrant, with the measure of angle K = 90°. Suppose triangle JKL is a 45°-45°-90° triangle and segment JK is one of the legs. What are the coordinates of point L?
7,2) see below
<jkl=245 degrees
Any letter , number and symbols on the keyboard
To determine the coordinates of point L, we need to know the specific coordinates of point J and the length of segment JK.
Since triangle JKL is a 45°-45°-90° triangle, it means that angles J and L are also 45° each.
Let's say the coordinates of point J are (x,y). Since segment JK is one of the legs and angles J and K are right angles, the length of segment JK is equal to the x-coordinate of point J.
Therefore, the coordinates of point K are (x, 0) because it lies on the x-axis. Point J has coordinates (x, y), and we can determine the coordinates of point L by using the properties of the 45°-45°-90° triangle.
In a 45°-45°-90° triangle, the lengths of the two legs are equal, and the length of the hypotenuse is equal to the length of the legs multiplied by √2.
Since segment JK is one of the legs, the length of JK is JK = x.
Therefore, the length of segment KL, which is also equal to segment JK, is KL = x.
To find the coordinates of point L, we need to move from point K, which has coordinates (x, 0), in the direction of angle L (45°). Since angle L is in the first quadrant, we need to move in a positive direction along both the x and y axes.
Using the properties of the 45°-45°-90° triangle, we know that the length of segment KL is x, and the slope from point K to point L is 1 (since both legs of the triangle are equal).
Therefore, to find the coordinates of point L, we need to add x to the x-coordinate of point K and y to the y-coordinate of point K.
Hence, the coordinates of point L are (x+x, 0+y) or (2x, y).