Answer:
- -9
- 2x + 3y = 21
- 4√5
Step-by-step explanation:
1. Put the point values in the equation where x and y are, then solve.
... 3(-2) -2k = 12
... -6 -2k = 12 . . . . eliminate parentheses
... -2k = 18 . . . . . . .add 6
... k = -9 . . . . . . . . . divide by -2
2. The perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. The equation for it can be found by swapping the x- and y-coefficients and negating one of them. Then, to make the line go through point (h, k), replace the constant with zero and replace x with (x-h) and y with (y-k).
... 2(x -6) +3(y -3) = 0 . . . . . a line through P perpendicular to PQ
... 2x + 3y = 21
3. The Pythagorean theorem is used for finding the lengths of line segments. The difference in coordinates between P and R is ...
... P - R = (6, 3) - (2, -5) = (6-2, 3-(-5)) = (4, 8)
The length of segment PR can be considered to be the length of the hypotenuse of a right triangle with these leg lengths.
... ║PR║ = √(4² +8²) = √80
... ║PR║ = 4√5
