Finding points on graph

Question

find all points having an x-coordinate of 4 whose distance from the point (-4,2) is 10. Find all the points.

 

 

not sure how to find the points

Answer 1

(1) Plot the point (-4,2)

 

(2) Run a line parallel to the y axis, x=4

 

(3) Run two lines from (-4,2) that intersect the line x=4.  One line will cross x=4 in the first quadrant, one will cross x=4 in the fourth quadrant.

 

(4) Run a line parallel to the y axis that goes through (-4,2).  This line will be y=2

 

(5) The lines x=4 and y=2 intersect at (4,2)

 

(6) You have two right triangles: one formed by the points (-4,2), (4,2) and (4, a) and the second formed by (-4,2), (4,2) and (4, b)

 

(7) the right triangles are 6, 8, 10 triangles  where 10 is the hypotenuse, 8 is the distance from (-4,2) and (4,2), and 6 is the distance from (4,2) up to (4, a) and the distance from (4,2) down to (4, b)

 

(8) your two points are (4,8) and (4,-4)

 

Denny Rose

Galion, OH

Answer 2

The set of points equidistant from a given point is a circle.  The given point is the center of the circle.  So the point (-4,2) is the center of a circle of radius 10.  In standard form. the circle's equation is:

 

(x-(-4))² + (y-2)² = 10²

(x+4)² + (y-2)² = 100

 

The circle will intersect the vertical line x=4 at two places:

 

(4+4)² + (y-2)² = 100

64 + (y-2)² = 100

(y-2)² = 36

√(y-2)² = √36

y-2 = ±6

 

y = 8 and -4

 

The two points are (4,-4) and (4,8).  Click on the link below to see the graph:

 

http://www.wyzant.com/resources/files/326766/intersection_of_circle_and_line/download?encryptedID=J4VnCa2KoUI%3D&d=v