Find the distance between the points (1, 2) and (4, 6).

Step 1: Identify the coordinates

First, we identify the coordinates of the two given points. Let the first point be $(x_1, y_1)$ and the second point be $(x_2, y_2)$.

Step 2: Recall the Distance Formula

To find the distance between two points in a coordinate plane, we use the distance formula. This formula is derived from the Pythagorean theorem.

Step 3: Substitute the coordinates into the formula

Now, we substitute the identified coordinates into the distance formula. We replace $x_1$ with 1, $y_1$ with 2, $x_2$ with 4, and $y_2$ with 6.

Step 4: Calculate the differences

Next, we perform the subtractions inside the parentheses: $4 - 1 = 3$ and $6 - 2 = 4$.

Step 5: Square the differences and add

Now, we square the results: $3^2 = 9$ and $4^2 = 16$. Then, we add these squared values together: $9 + 16 = 25$.

Step 6: Calculate the square root

Finally, we take the square root of 25, which gives us 5. This is the distance between the two given points.

More from this chapter

• The x-coordinate of the point which lies on the line represented by 3x - y - 1 = 0 and whose y-coordinate is 5, is:
• Show that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square.
• The distance of ( - 4, 7) from y-axis is:
• Find the equations of the lines parallel to axes and passing through ( -2, 3).
• In the Cartesian coordinate plane shown, plot the points A(2,3), B(-2,-1), and C(2,-3), and connect them in order A→ B→ C. Then find the area of ABC.
• Find the distance between the points (3, 4) and (-3, -4).

All Orienting Yourself: The Use of Coordinates solutions →