Find the distance between the points A(5, 9) and B(3, 11).

Step 1: Identify the coordinates

First, we identify the coordinates of the two given points. Point A has coordinates $(x_1, y_1) = (5, 9)$ and Point B has coordinates $(x_2, y_2) = (3, 11)$. These values will be used in the distance formula.

Step 2: Apply the distance formula

To find the distance between two points in a Cartesian plane, we use the distance formula. This formula is derived from the Pythagorean theorem and calculates the length of the line segment connecting the two points.

Step 3: Substitute the values

Now, we substitute the identified coordinates into the distance formula. We replace $x_1$ with 5, $y_1$ with 9, $x_2$ with 3, and $y_2$ with 11.

Step 4: Calculate the differences

Next, we perform the subtractions inside the parentheses. $(3 - 5)$ becomes $-2$, and $(11 - 9)$ becomes $2$.

Step 5: Square the differences

Now, we square the results from the previous step. $(-2)^2$ is $4$, and $(2)^2$ is also $4$.

Step 6: Sum and find the square root

Finally, we sum the squared values to get $8$, and then find the square root of $8$. The square root of $8$ can be simplified to $2\sqrt{2}$.

More from this chapter

• Q7. If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b. [2 Marks]
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• Find a point on the y-axis that is at the same distance from the points (-5, 2) and (9, -2).
• Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.
• Find the relation between x and y if the point (x, y) is equidistant from (7, 1) and (3, 5).
• 1. Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b)
• Find the coordinates of the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).
• Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis, and find the coordinates of the point of division.

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