Question

In the xy-plane, line m has a slope of 2 and crosses the x-axis at the point (5/2, 0). Line n is perpendicular to line m and crosses the y-axis at the point (0, -5/2). At what point do lines m and n intersect?
A) (5/2, -5/2)
B) (4, -2)
C) (1, -3)
D) (2, -5/2)

Answer 1

Since line m has a slope of 2 and crosses the x-axis at (5/2, 0), we can write the equation of line m in point-slope form as y - 0 = 2(x - 5/2).
Simplifying this equation, we get y = 2x - 5.

Since line n is perpendicular to line m, the slope of line n is the negative reciprocal of the slope of line m, which is -1/2.
Since line n crosses the y-axis at (0, -5/2), we can write the equation of line n in point-slope form as y - (-5/2) = -1/2(x - 0).
Simplifying this equation, we get y = -1/2x - 5/2.

To find the point of intersection of line m and line n, we can solve the system of equations:
y = 2x - 5 (equation of line m)
y = -1/2x - 5/2 (equation of line n)

Setting the two equations equal to each other, we get:
2x - 5 = -1/2x - 5/2.

Adding 1/2x to both sides and adding 5/2 to both sides, we get:
2x + 1/2x = -5/2 + 5/2.

Combining like terms, we get:
5/2x = 0.

Dividing both sides by 5/2, we get:
x = 0.

Plugging this value of x back into either equation, we can solve for y:
y = 2(0) - 5,
y = -5.

Therefore, the point of intersection of line m and line n is (0, -5).

Thus, the answer is not listed.