SAT - Math - Coordinate geometry
A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line? (more)
A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle? (more)
x2 20x y2 16y = −20
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?
C) (10, 8)
Line l passes through the origin and makes 300 with the positive x axis.
find the equation of line l.
a) y = x\2
b) y = x\root 2
c) y= x\root 3
d)y= (root 2) x
e) y= (root 3) x
general equation of a line is y = mx + c where m is gradient and c is y intercept m = tan(30) m = 1/√3 coordinates if the origin is (0,0) Putting that in the gen eqn We have 0 = (1/√3) . 0 + c C = 0 So then , the eqn of the line is y = (1/√3)x
3 points lie on an xy plane, with each point representing where a particular person lives. Amy lives at point (2,3); Brian lives at point (0,7); and Claire lives at point (-2,3). They all wish to meet up with each other for lunch, but at a location that is equidistant from each of their respective houses. At what point do they meet?
The point equidistant from 3 points in a coordinate plane would be the circumcenter of the triangle formed by the three points.
Circumcenter is the intersection point of the perpendicular bisectors of the sides of the triangle.
Equation perpendicular bisector of (2,3) and (0,7)
(x-2)2 + (y-3)2 = (x-0)2 + (y-7)2
simplyfing and canceling second order terms
4 - 4x + 9 - 6y = 49 - 14y
4x - 8y +36 = 0
Similarly Equation of perpendicular bisector of (2,3) and (-2,3)
(x-2)2 + (y-3)2 = (x+2)2 + (y-3)2
(x-2)2 = (x+2)2
only solution x = 0
simultaneously solving both equations
put x = 0 in first equation
8y = 36
y = 9/2
required point: (0,4.5)