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About distance betweentwo points

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- DISTANCE BETWEEN TWO POINTS PRECIOUS FRAULEIN RODA CASSANDRA TAGULALAP SHAINA MAE FADERON
- DISTANCE BETWEEN TWO POINT The distance between two points is always nonnegative. It is positive when the two points are different, and zero if the points are the same. If P and Q are two points, then the distance from P to Q is the same as the distance from Q to P. That is, PQ = QP. Consider two points that are aligned horizontally or vertically on the coordinate plane. The horizontal distance between these points is the absolute value of the difference of their -coordinates. Likewise, the vertical distance between these points is the absolute value of the difference of their y- coordinates.
- EXAMPLE 1: FIND THE DISTANCE BETWEEN P(3,2) AND Q(10,2). Since P and Q are aligned horizontally, then PQ=|10-3| or PQ=7
- EXAMPLE 2: DETERMINE THE DISTANCE BETWEEN A(4,3) AND B(4,-5). Points A and B are on the same vertical line. So the distance between them is AB=|3-(-5). This can be simplified to AB =|3+5| or AB=8.
- THE DISTANCE FORMULA The distance between two points, whether or not they are aligned horizontally or vertically, can be determined using the distance formula. Consider the points P and Q whose coordinates are (X1, 1) and (X2, 2), respectively. The distance d between these points can be determined using the distance formula or
- EXAMPLE 1: FIND THE DISTANCE BETWEEN P(1,3) AND Q(7,11). Solution: To find the distance between P and Q, the following procedures can be followed. 1. Let (x1,y1) = (1,3) and (x2,y2) = (7,11). 2. Substitute the corresponding values of x1, y1, x2, and y2 in the distance formula 3. Solve the resulting equation. . Add a. The distance between P and Q is 10 units.
- EXAMPLE 2: DETERMINE THE DISTANCE BETWEEN A(1,6) AND B(5,-2). Solution:Let x1= 1, y1=6, x2=5, and y2= -2. Then substitute these values in the formula
- EXAMPLE 3: A map showing the locations of different municipalities and cities is drawn on a coordinate plane. Each unit on the coordinates plane is equivalent to 6 kilometers. Suppose the coordinates of Mabini City is (2,2) and Sta. Lucia town is (6,8). What is the shortest distance between these two places?
- SOLUTION: Let x1=2, y1 =2, x2 =6, and y2 =8. Then substitute these values into the distance formula Simplify the expression.

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