Slope
Find the slope of the line passing through the points (3, 2) and (7, 10)
m=(y2-y1)/(x2-x1) -> (10-2)/(7-3) = 8/4 =2
Find the distance between the points (−2, 3) and (4, −1)
Δx=6, Δy=−4⇒d=root (6^2+(−4)^2)= root(36+16)= root(52)=2*root(13)
Find the midpoint of the segment joining (−4, 6) and (8, −2)
M((−4+8)/2,(6+(−2))/2)=M(2,2)
Write the equation of a circle with center (−2, 5) and radius 4
(x+2)^2+(y−5)^2=16
Write the equation of the line passing through (2, −1) that is parallel to y=3x+4y.
y- (-1) = 3(x-2) -> y+1=3x-6 -> y-3x-7
Calculate the distance between (1, 2) and (5, 9), rounding to two decimal places
Δx=4, Δy=7⇒d=root(16+49)=root(65)
Determine the midpoint of the line segment with endpoints (3, 7) and (9, −5)
M((3+9)/2,(7+(−5))/2)=M(6,1).
Find the center and radius of the circle given by (x+3)^2+(y−4)^2=16
Radius = distance between center and point = 7−3=47-3=47−3=4.
Equation: (x−3)2+(y+2)2=16
Write the equation of the line passing through (4, 5) that is perpendicular to y=(−1/2)x+7y.
y-5 = 2(x-4) -> y-5=2x-8 -> y=2x-3
Find the distance between (7, 2) and (1, 6) using the distance formula
Δx=−6, Δy=4⇒d=root(36+16)=root(52)=2* root(13)
A line segment has endpoints (−3, −7) and (1, 5). What is the midpoint?
M((−3+1)/2,(−7+5)/2)=M(−1,−1)
The equation of a circle is (x−h)^2+(y−k)^2=49 If the center is at (−5, 2), write the full equation of the circle.
(x+5)^2+(y−2)^2=49