In Exercises 33-36, determine whether the lines through the two of points are pa
ID: 2894903 • Letter: I
Question
In Exercises 33-36, determine whether the lines through the two of points are parallel or perpendicular (6, -1) and (4, 3): (-5, 2) and (-7, 6) (-3, 9) and (4, 4): (9, -1) and (4, -8) (-1, -4) and (2, 3): (-5, 2) and (-19,8) (a, -2b) and (3a, 6b): (2a, -6b) and (5a, 0) In Exercises 37-40, determine the value of k. The distance between (-1, 3) and (11, k) is 13. The distance between (k, 0) and (0, 2k) is 10. Points (6, -1), (3, k), and (-3, -7) are on the same line. The points in Exercise 39 are the vertices of a right triangle, the right angle at (3, k). In Exercises 41-44, show that the given points are vertices given geometric figures (2, 3), (4, 9), and (-2, 7) are vertices of an isosceles triangle (-1, 3), (3, 5), and (5, 1) are the vertices of a right triangle. (-5,-4), (7, 1), (10, 5), and (-2, 0) are the vertices parallelogram (-5, 6), (0, 8), (-3, 1), and (2, 3) are the vertices of a square In Exercises 45-48, find the indicated areas and perimeters. Find the area of the triangle in Exercise 42.Explanation / Answer
39.
First undertand that the slope between any two points on the same line will always be the same.rom
thus,
Slope from (6,-1) and (3,k) = (k+1)/(3-6) => -(k+1)/3
Slope from (6,-1) and (-3,-7) = (-7+1)/(-3-6) => -6/-9 => 2/3
equating both slopes:
k+1 = -2
k = -3