Find the distance between point M(−4, 3) and N(9, −2). Round your answer to the nearest tenth
Using the distance formula, the distance between point M(-4, 3) and N(9, -2) can be found as follows:
d = sqrt((9 - -4)^2 + (-2 - 3)^2)
= sqrt((13)^2 + (-5)^2)
= sqrt(169 + 25)
= sqrt(194)
≈ 13.9
Rounded to the nearest tenth, the distance between M(-4, 3) and N(9, -2) is approximately 13.9 units.
To find the distance between two points, we can use the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Given that M has coordinates (-4, 3) and N has coordinates (9, -2), we can substitute these values into the formula:
Distance = √((9 - (-4))² + (-2 - 3)²)
Simplifying the expression inside the square root:
Distance = √((9 + 4)² + (-2 - 3)²)
Distance = √(13² + (-5)²)
Distance = √(169 + 25)
Distance = √194
Rounding to the nearest tenth:
Distance ≈ 13.9
Therefore, the distance between M(-4, 3) and N(9, -2) is approximately 13.9 units.
To find the distance between two points on a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be used to find the distance between two points (x1, y1) and (x2, y2):
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point M are (-4, 3) and the coordinates of point N are (9, -2).
Plugging these values into the distance formula:
Distance = √((9 - (-4))^2 + (-2 - 3)^2)
= √((9 + 4)^2 + (-2 - 3)^2)
= √(13^2 + (-5)^2)
= √(169 + 25)
= √194
Rounding the answer to the nearest tenth:
Distance ≈ √194 ≈ 13.928
Therefore, the distance between point M(-4, 3) and N(9, -2) is approximately 13.9 units.