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?
That triangle could be anywhere in the first quadrant and you have not told us the length of any side of the triangle.
j(2.7) point
k(2,2) point
and the answers are,
a(-2,2)
b(6,2)
c(7,2)
d(-3,2)
L could be 5 units to the right of K or to the left of K at the same level or y coordinate
so L could be (7,2) or L could be (-3,2)
However (-3,2) is not in the first quadrant
so
(7,2)
To find the coordinates of point L in triangle JKL, we need to start with the coordinates of point J and use the properties of a 45°-45°-90° triangle.
Since triangle JKL is in the first quadrant and angle K is 90°, we know that point K is at coordinates (x, 0), where x is the x-coordinate of point J.
In a 45°-45°-90° triangle, the two legs (segments JK and KL in this case) are congruent, and the length of the hypotenuse is √2 times the length of the leg. Since segment JK is one of the legs, we can assume its length is 1.
So, we have the coordinates of point J as (x, y) and the length of JK as 1. Using the properties of a 45°-45°-90° triangle, we can determine the length of KL.
The length of KL is √2 times the length of JK, which means KL is √2. Therefore, segment KL has length √2.
Since point K is at (x, 0) and KL has length √2, the coordinates of point L will be (x, -√2). Therefore, the coordinates of point L in triangle JKL are (x, -√2).