Finding Segment Length Using Coordinates
To find the length of the segment joining two points, we use the distance formula derived from the Pythagorean theorem.
Distance Formula Application
The coordinates of the two points are $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (4, 6)$.
The distance formula is:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Calculation Steps
- Calculate the difference in the x-coordinates:
$ \Delta x = x_2 - x_1 = 4 - 1 = 3 $
- Calculate the difference in the y-coordinates:
$ \Delta y = y_2 - y_1 = 6 - 2 = 4 $
- Square these differences:
$ (\Delta x)^2 = 3^2 = 9 $
$ (\Delta y)^2 = 4^2 = 16 $
- Add the squared differences:
$ (\Delta x)^2 + (\Delta y)^2 = 9 + 16 = 25 $
- Take the square root of the sum:
$ d = \sqrt{25} = 5 $
The length of the segment joining (1,2) and (4,6) is 5.
Similar Questions
- What is the equation of line through (1,2) and (3,8)
- A right triangle has vertices at P(0, 0), Q(8, 0), and R(0, 6). What are the coordinates of its Circumcenter?
- Find the x-intercept of $5x + 2y = 10$
- Point P is at an equal distance from the three vertices of a triangle with coordinates A(0, 0), B(4, 0), and C(0, 3). What are the coordinates of point P?
- Find slope of the line passing through points (-2,5) and (4,-7).
- In a triangle with vertices P(x, y), Q(5, -1), and R(2, 6), the Centroid is at G(4, 2). What are the coordinates of vertex P?
- In triangle ABC, an altitude AD is drawn from point A to side BC. Given the coordinates A(1, 5), B(2, 1), and C(6, 3), what is the slope of the line representing altitude AD?
If line passing through (3,-1) with slope 4; find y-intercept.
Important Questions from Coordinate Geometry
What is the reflection of the point (-1, 5) in the line x = 1?
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
Slope of the line AB is 4/3. Co-ordinates of points A and B are (x, -5) and (2, -3) respectively. What is the value of x?
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
