Question

the slope of the line containing the points (-5, 3) and (-2, 1) is -2/3 2/3 -3/2 user: the slope of a line that is perpendicular to a line whose slope is 3/8 is -8/3 3/8 8/3 user: the equation of the line through point (- 4, 0) and parallel to the y-axis is x = -4 y = -4 x y = -4 user: the equation of circle having a diameter with endpoints (-3, 1) and (5, 7) is (x - 4)² (y - 3)² = 25 (x - 1)² (y - 4)² = 25 (x - 1)² (y - 4)² = 100 user: a square has symmetry with respect to a ...

Answer 1

Slope = (y2 - y1)/(x2 - x1) = (1 - 3)/(-2 - (-5)) = -2/(-2 + 5) = -2/3

For perpendicular lines, m2 = -1/m1 = -1/(3/8) = -8/3

A line passing through point (-4, 0) and parallel to the y-axis is x = -4

$diameter=\sqrt{(7-1)^2+(5+3)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10$
radius = diameter/2 = 10/2 = 5
center of circle = midpoint of diameter = ((-3 + 5)/2, (1 + 7)/2) = (2/2, 8/2) = (1, 4)
Required equation is (x - 1)^2 + (y - 4)^2 = 5^2
(x - 1)^2 + (y - 4)^2 = 25