A coordinate system is superimposed over a map of Washington, D.C. Jessica and Omar walk from the Metro Center to 15th Street and then up 15th Street to McPherson Square. How far is the Metro center from McPherson Square? This problem will be solved in Example 2.
Recall that subtraction is used to find the distance between
two points that lie on a vertical or horizontal line.
In the following activity, you will find the distance between
two points that do not lie on a horizontal or vertical line.
In the activity, you discovered that (MN)2 +
(MP)2 = (NP)2. You can solve this equation
for MN to find the distance between points M and N.
The Distance
Formula can be used to find the distance between any two points (x1,
y1) and (x2, y2).
1. Find the distance between points A(1,
2) and B(–3, 7).
Alternative Solutions:
Example
Map
Link
2. Refer to the application at the
beginning of the lesson. The Metro Center is located 4 blocks east of the
intersection of 15th Street and G Street. McPherson Square is located
2 blocks north of the intersection. How far is the Metro Center from McPherson
Square?
Alternative Solutions:
Let
the Metro Center be represented by (4, 0) and McPherson Square by (0, 2). So, x1
= 4, y1 = 0, x2 = 0, and y2
= 2.
The Metro
Center is about 4.5 blocks from McPherson Square.
Suppose you know the coordinates of a point, one coordinate
of another point, and the distance between the two points. You can use the
Distance Formula to find the missing coordinate.
Example
3. Find the value of a if G(4,
7) and H(a, 3) are 5 units apart.
Alternative Solutions:
The value
of a is 7 or 1.
Sumber
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