CPM Homework Help : PC Problem 12-42

Recall from Chapter 1 that the line through the points A and B can be described by the vector equation for −∞ < t < ∞. Homework Help ✎
1. Let A = (2, 4) and B = (1, −3). Since = 2i + 4j and = −i − 7j, verify that in this case + t() = 2i + 4j + t(−i − 7j).
2. Rewrite this expression as ( )i + ( )j.
3. Show that this line goes through the point (0, −10).

Hint (a):

Use substitution.

Hint (b):

Use the distributive property, then combine like terms.

Step (b):

2i + 4j + t(−i −7j)
= 2i + 4j −ti −7tj
= 2i −ti + 4j −7tj

Hint (c):

If (0, 10) is on the line, then 0i + 10j is possible.

Step (c):

(2 − t)i + (4 − 7t)j = 0i + 10j

Step (c):

2 − t = 0 4 − 7t = 10

Does t have the same value in both equations?
If it is on the line, then it should.