Final answer:
The length of segment PQ is 5sqrt(10), the midpoint is (1/2, -3/2), the slope is 1/3, and the equation of line PQ is y = (1/3)x - 5/3. Hence the correct answer is option A
Step-by-step explanation:
To find the length of segment PQ, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
By substituting the values of the endpoints P(-7, -4) and C(8, 1), we get:
d = sqrt((8 - (-7))^2 + (1 - (-4))^2)
d = sqrt(15^2 + 5^2)
d = sqrt(225 + 25)
d = sqrt(250)
d = 5sqrt(10)
To find the midpoint of segment PQ, we can use the midpoint formula:
((x1 + x2)/2, (y1 + y2)/2)
By substituting the values of the endpoints P(-7, -4) and C(8, 1), we get:
((-7 + 8)/2, (-4 + 1)/2)
((1/2, -3/2)
The slope of line PQ can be found using the formula:
m = (y2 - y1)/(x2 - x1)
By substituting the values of the endpoints P(-7, -4) and C(8, 1), we get:
m = (1 - (-4))/(8 - (-7))
m = 5/15
m = 1/3
The equation of line PQ can be found using the slope-intercept form:
y = mx + b
By substituting the value of the slope (m = 1/3) and the coordinates of one of the endpoints (P(-7, -4)), we get:
y = (1/3)x + b
-4 = (1/3)(-7) + b
-4 = -7/3 + b
b = -4 + 7/3
b = -12/3 + 7/3
b = -5/3
Therefore, the equation of line PQ is y = (1/3)x - 5/3.
Hence the correct answer is option A