To find the points that have a distance of 10 from the point (-1, 2), we can use the distance formula. Let's call the unknown points (x, y).
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values from the given point (-1, 2) and the distance of 10 into the formula:
10 = √((x - (-1))^2 + (y - 2)^2)
Simplifying:
100 = (x + 1)^2 + (y - 2)^2
Expanding:
100 = x^2 + 2x + 1 + y^2 - 4y + 4
Rearranging and combining like terms:
x^2 + y^2 + 2x - 4y + 105 = 0
This is the equation of a circle centered at (-1, 2) with a radius of 10.
The points that have a distance of 10 from the point (-1, 2) lie on the circumference of this circle.
Which of the following points has a distance of 10 from the point (−1, 2) ?
1 answer