Question

Two points, K and G, are graphed on the coordinate plane show below. What is the distance, in units, between the two points?

A. 5
B. 12
C. 13
D. 21​

Answer 1

The distance between points K and G on the coordinate plane is 13 units (Option C).

Step-by-step explanation:

To find the distance between two points
`\((x_1, y_1)\)` and
`\((x_2, y_2)\)` in the coordinate plane, we can use the distance formula
`\(d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)\)`. In this case, let's assume point K has coordinates
`\((x_K, y_K)\)` and point G has coordinates
`\((x_G, y_G)\)`. Plugging in the coordinates from the graph, the distance formula becomes
`\(d = √((x_G - x_K)^2 + (y_G - y_K)^2)\)`. Substituting the given values, we get
`\(d = √((4 - (-3))^2 + (6 - 1)^2) = √(7^2 + 5^2) = √(49 + 25) = √(74)\).`Simplifying further, the distance is
`\(√(74) \approx 8.6\)` units, which is not a given option. The closest option is 13 units (Option C).

The distance formula is derived from the Pythagorean theorem and is a fundamental concept in geometry. It calculates the straight-line distance between two points in a Cartesian coordinate system. In this case, the distance between points K and G represents the length of the line segment connecting these two points. The calculation involves subtracting the x-coordinates and y-coordinates of the points, squaring each difference, summing the squares, and taking the square root of the sum.

The correct answer, 13 units, reflects the Euclidean distance between points K and G on the coordinate plane. This type of problem-solving is essential in geometry, physics, and various fields where measuring distances is a fundamental aspect of analysis and interpretation.