Geometrical question?

When lines are perpendicular, their slopes are negative reciprocals of each other.

m1 = (1 - 0) / (2 - 0) = 1/2

m2 = -1 / m1 = -1 / (1/2) = -2

y = m2 * x + b

Substitute the given points:

1 = -2 * 1 + b

t = -2 * 0 + b

Two equations with two unknowns, solve for t.

Start by finding the slope of each line. Recall that the slope, m, is (y2 - y1)/(x2 - x1), where y2 is the second y-coordinate, y1 is the first y-coordinate, etc. (normally these world be written as subscripts). Also recall that when two lines are perpendicular, the slope of one is the negative reciprocal of the other (i.e -1/m)

Line l:

ml = (1 - 0) / (2 - 0)

ml = 1 / 2

Find the slope, mq, of line q by taking the negative reciprocal of the ml we found above:

mq = -1/(ml) -- equation for mq

mq = -1/(1/2) -- plug in ml

mq = -1 * (2/1) -- multiply by the reciprocal (this is the same as diving by 1/2, but much easier!)

mq = -1 * 2 -- simplify fraction

mq = -2 -- multiply

Now plug in the slope of line q and the coordinates of line q and solve for t:

-2 = (t - 1) / (0 - 2)

-2 = (t - 1) / -2

4 = t - 1

5 = t

Check your work to make sure it comes out right. If we use the formula of the slope with our new t, we should get -2:

mq = (5 - 1) / (0 - 2)

mq = 4 / -2

mq = -2

Our answer checks out!

(NOTE: I will use capital letters for your lines rather than lower case...)

The slope of line L = 1/2.

The slope of line Q = (t - 1)/(0 -2), or (1 - t)/2

Since perpendicular lines have slopes that are negative reciprocals of each other, we must have:

Slope of line Q = - 1/slope of line L --> (1 - t)/2 = - 2 --> (1 - t) = - 4 --> t = 5 (choice e)

It's e. 5