Question

Isosceles triangle JKL has a perimeter of 16 with the following vertices:
J(5,-2)
K(2,2)
L(x, 2)
What is the x-coordinate for point L?

Answer 1

The Isosceles triangle JKL has two equal sides

The x-coordinate of point L is 2 or 8

How to determine the x-coordinate of L

The coordinates of the triangle are given as:

J = (5,-2)

K = (2,2)

L = (x, 2)

Start by calculating the distance between the vertices using the following distance formula

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$JK = \sqrt{(5 -2)^2 + (-2 -2)^2} = 5$

$KL = \sqrt{(2 -x)^2 + (2 -2)^2} = 2 -x$

$JL = \sqrt{(5 -x)^2 + (-2 -2)^2} = \sqrt{(5 -x)^2 + 16}$

The triangle is an isosceles triangle.

So, we have:

JK = JL

The equation becomes

$\sqrt{(5 - x)^2 + 16} = 5$

Take the square of both sides

$(5 - x)^2 + 16 = 25$

Subtract 16 from both sides

$(5 - x)^2 = 9$

Take the square root of both sides

$5 - x = \pm3$

Solve for x

$x = 5 \pm 3$

x = 2, or 8

Hence, the x-coordinate of point L is 2 or 8

Read more about isosceles triangles at:

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