Locus Equidistant from Two Points Worksheets

How to Find the Locus of Points Equidistant from Two Points - Before we learn how to find out the locus of points equidistant from two points, we must learn the concept behind it. The locus of two points is the perpendicular bisector of the line segment with these two points as endpoints. However, to find the locus of points, there are two methods to resolve them. The first method is by using the distance formula. Let us take an example. Point (x, y) is equidistant from points (8, -1) and (2, 9). We know that the distance of (x, y) to (8, -1) = distance from (x, y) to (2, 9). Method 1: √((x-2)2 + (y-9)2) = √((x - 8)2+ (y + 1)2 ) (x-2)2+(y - 9)2 = (x - 8)2+(y + 1)2 x2-4x + 4 + y2-18y + 81= x2-16x + 64 + y2 + 2y + 1. -4x - 18y + 85 = -16x + 2y + 65. 12x - 20y + 20 = 0. 3x - 5y+ 5 = 0. The second method is to find the perpendicular bisector: Midpoint = ((2+8)/2, (9–1)/2) = (5,4). The slope of the line: (-1-9)/(8–2) = -10/6 = -5/3. Perpendicular bisector has slope = 3/5 and passes through the point (5, 4). y-4 = 3/5(x - 5), 5(y - 4) = 3(x - 5), 5y - 20 = 3x - 15, 3x - 5y + 5 = 0.

• Basic Lesson

Guides students through the application of coordinates. What is the equation of the locus of points equidistant from the points (-5, 3) and (3, 3)? The locus of points will be a straight line halfway between the two points. In this problem, the distance between the points is 8 units, so the line is drawn so that it is 4 units from each point. The equation of the line will be x = -1.

• Intermediate Lesson

Demonstrates how to use loci in real world applications. 2 houses are 100 feet apart. A street to be constructed such that the distance from any point on the street to each house is always the same distance. Describe where the street should be constructed.

• Independent Practice 1

A really great activity for allowing students to understand the concepts of the Locus Equidistant from Two Points. Two pillars are 10 m apart. A curtain is to be placed between 2 pillars such that the distance from any point on the curtain to each pillar is always the same distance. Describe where the curtain should be placed.

• Independent Practice 2

Students use Locus Equidistant from Two Points in 20 assorted problems. The answers can be found below. There are two flowerbeds. Peter walks so that he is always equidistant from both flowerbeds. Describe his path.

• Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Locus Equidistant from Two Points.

• Skill Quiz

This tests the students ability to understand Locus Equidistant from Two Points.