how to find the distance between the points P(7,5) and Q(2,5) Related: Distance Formula?

Question

how to find the distance between the points P(7,5) and Q(2,5) Related:  Distance Formula?

Answer

Root under ( x2 - x1 )^2 + ( y2 - y1 )^2 Root under ( 2 - 7 )^2 + ( 5 - 5 )^2 Root under ( - 5 )^2 + (0)^2 Root under 25 + 0 Root under 25 = 5 units

Answer

The answer is 5 units- because by using distance formula =
√(x1-x2) ^2+(y1-y2)^2=√(7-2)^2+(5-5)^2=√25=5units

Answer

Answer

To find the distance between the points P(7,5) and Q(2,5), you can use the Distance Formula. Here’s a detailed explanation:
Understanding the Distance Formula
The Distance Formula is derived from the Pythagorean theorem and is used to calculate the distance between two points in a Cartesian coordinate system. The formula is:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Where:
- (x1, y1) and (x2, y2) are the coordinates of the two points.
Identifying the Coordinates
For points P(7,5) and Q(2,5):
- P has coordinates (x1, y1) = (7, 5)
- Q has coordinates (x2, y2) = (2, 5)
Applying the Distance Formula
Now, substitute the values into the Distance Formula:
1. Calculate the difference in x-coordinates:
- (x2 - x1) = (2 - 7) = -5
2. Calculate the difference in y-coordinates:
- (y2 - y1) = (5 - 5) = 0
3. Substitute into the formula:
- Distance = √[(-5)² + (0)²]
- Distance = √[25 + 0]
- Distance = √25
- Distance = 5
Conclusion
The distance between points P(7,5) and Q(2,5) is 5 units. This means that the two points lie on a horizontal line, and the distance is simply the difference between their x-values.

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