a triangle has one side that lies along the line y=1/4x and another that lies along the line y=(-1/4)x. which of the following points could be a vertex of the triangle?
a. (4,4)
b. (0,0)
c. (-4,-2)
d. (1,8)
well, (0,0) lies on both lines, so it's a likely candidate, no?
To determine which of the given points could be a vertex of the triangle, we need to find the intersection points of the two lines that represent the sides of the triangle.
Let's find the intersection point of the line y = 1/4x and y = -1/4x:
1/4x = -1/4x (since both lines intersect at the same point, the x-coordinate of both equations must be the same)
(1/4 + 1/4)x = 0
(2/4)x = 0
x/2 = 0
x = 0
Now, substitute this value back into either of the equations to find the y-coordinate:
y = 1/4 * 0
y = 0
Therefore, the intersection point is (0, 0).
Next, we'll check if each of the given points lies on the lines y = 1/4x and y = -1/4x. We can substitute the x and y coordinates of each point into these equations to check if they satisfy them.
a. (4, 4)
Substituting into y = 1/4x: 4 = 1/4 * 4 = 1
4 does not equal 1, so (4, 4) is not a vertex of the triangle.
b. (0, 0)
Substituting into y = 1/4x: 0 = 1/4 * 0 = 0
0 equals 0, so (0, 0) could be a vertex of the triangle.
c. (-4, -2)
Substituting into y = 1/4x: -2 = 1/4 * -4 = -1
-2 does not equal -1, so (-4, -2) is not a vertex of the triangle.
d. (1, 8)
Substituting into y = 1/4x: 8 = 1/4 * 1 = 1/4
8 does not equal 1/4, so (1, 8) is not a vertex of the triangle.
Therefore, the only point that could be a vertex of the triangle is (0, 0). The correct answer is b. (0, 0).