Answer:
O (0,0)
R (k, k)
S (k, 2k)
T (2k, 2k)
U (k, 0)
OT = 2√2 + 2k
Step-by-step explanation:
Since the entire shape is 2k units, the height is 2k.
The length of SU is the height. SU = 2k
SU is made of two lines called SR and RU, both the same length.
If SU = SR + RU and SR = RU, they are half of 2k. SR = RU = k
Other lines that have the same length as RU and SR is OU and ST. They all have the one tick marking which means equal length.
SR = RU = OU = ST = k
We know the coordinates of point O. It is the origin because it's where the x-axis and the y-axis intersect. O (0,0)
Since OU=k, U is k units to the right of O for it's x-coordinate. U is still on the x-axis so it's y-coordinate is 0. U (k, 0)
Since R is k units above U, increase the y-coordinate by k. R (k, k)
Point S is k units above R, increase the y-coordinate by k. S (k, 2k)
Point T is k units to the right of S. Increase the x-coordinate by k, and the y-coordinate does not change. T (2k, 2k)
The length of <u>OT is double the hypotenuse of one of the right triangles</u>.
Use the Pythagorean theorem to find the hypotenuse of triangle STR.
RT² = ST² + SR²
RT² = k² + k² <=substitute the lengths you know
RT² = 2k² <=find the square root of both sides
RT = √(2)k
Since triangles STR and ORU are the same, hypotenuse RT is the same as hypotenuse OR.
OT = 2(√(2)k)
OT = 2√2 + 2k
