Question

I am a right isosceles triangle. i have an area of 18 square units. the coordinates of the vertex at which the two congruent sides meet is (0, 0) and my sides form horizontal and vertical lines. do you have enough information to determine the coordinates of my two possible remaining vertices?if so, find them. (if there is not enough information enter not enough.)

a) Yes, the coordinates are (6, 0) and (0, 6).
b) Yes, the coordinates are (-6, 0) and (0, -6).
c) Not enough information.
d) No, it's impossible to determine the coordinates.

Answer 1

By calculating the side length from the given area of an isosceles right triangle and considering the orientation of the sides along the coordinate axes, the remaining vertices are found to be either (6, 0) and (0, 6) or (-6, 0) and (0, -6).

Step-by-step explanation:

To determine the coordinates of the remaining vertices of the right isosceles triangle with an area of 18 square units and one vertex at the origin (0, 0), we start by recalling that the area (A) of a triangle is given by ½ × base × height. For an isosceles right triangle, the base and height are equal, thus A = ½ × side × side. To find the length of the side, we set up the equation 18 = ½ × side² and solve for the side which gives us a side length of 6 units. In a coordinate plane, considering the vertex at the origin, and the sides forming horizontal and vertical lines, the possible coordinates for the two other vertices are either horizontally to the right and vertically upward in the coordinate system, or horizontally to the left and vertically downward in the coordinate system. Thus, we have two sets of possible coordinates for the remaining vertices, which are either (6, 0) and (0, 6) or (-6, 0) and (0, -6).