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?
j(2.7) point
k(2,2) point
and the answers are,
a(-2,2)
b(6,2)
c(7,2)
d(-3,2)
(7,2) see below
To find the coordinates of point L in the 45°-45°-90° triangle JKL, we will use the information provided about points J and K.
Point J is given to be (2.7, ?) and point K is given to be (2, 2). Since triangle JKL is in the first quadrant and angle K is 90°, we know that point L must have positive x-coordinate and positive y-coordinate.
Since JKL is a 45°-45°-90° triangle, the length of both legs JK and KL are equal. Also, the length of the hypotenuse JL is equal to √2 times the length of either leg.
Given point J as (2.7, ?) and point K as (2, 2), we can calculate the length of JK using the distance formula.
Length of JK = √((x2 - x1)^2 + (y2-y1)^2)
= √((2.7 - 2)^2 + (2 - ?)^2)
To solve for ?, we find the length of JK using the above formula:
Length of JK = √((2.7 - 2)^2 + (2 - ?)^2)
= √((0.7)^2 + (2 - ?)^2)
Since JK and KL are equal in length, we can use the length of JK to find the coordinates of point L.
Given that JK is the leg of the triangle and length of JK is √((0.7)^2 + (2 - ?)^2), we can calculate the coordinates of point L:
To find the x-coordinate of L, add the length of JK to the x-coordinate of K.
x-coordinate of L = 2 + √((0.7)^2 + (2 - ?)^2)
To find the y-coordinate of L, add the length of JK to the y-coordinate of K.
y-coordinate of L = 2 + √((0.7)^2 + (2 - ?)^2)
Since no value for ? is given, we cannot determine the exact coordinates of point L without more information.