what is the distance between (4, -2) and (5, 4)
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (4, -2) and (5, 4).
So, x1 = 4, y1 = -2, x2 = 5, y2 = 4
Substitute these values into the distance formula:
Distance = sqrt((5 - 4)^2 + (4 - (-2))^2)
Distance = sqrt(1^2 + 6^2)
Distance = sqrt(1 + 36)
Distance = sqrt(37)
Therefore, the distance between the points (4, -2) and (5, 4) is sqrt(37) units.
sorry i meant to say what is the distance between (4, -2) and (-5, 4)
To find the distance between points (4, -2) and (-5, 4), we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = 4, y1 = -2, x2 = -5, y2 = 4
Substitute these values into the formula:
Distance = sqrt((-5 - 4)^2 + (4 - (-2))^2)
Distance = sqrt((-9)^2 + (6)^2)
Distance = sqrt(81 + 36)
Distance = sqrt(117)
Distance ≈ 10.82
Therefore, the distance between the points (4, -2) and (-5, 4) is approximately 10.82 units.
How can you tell if a triangle is a right triangle with one 90 degree angle? Choose the best answer.
To determine if a triangle is a right triangle with one 90-degree angle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, to check if a triangle is a right triangle with one 90-degree angle, you can calculate the squares of the lengths of the three sides and see if they satisfy the Pythagorean theorem.
If the sum of the squares of the lengths of two shorter sides is equal to the square of the length of the longest side, then the triangle is a right triangle with one 90-degree angle.
Another way is to use the slopes of the sides of the triangle. If two sides have slopes that are negative reciprocals of each other, then the triangle is a right triangle with a 90-degree angle. This is because the slopes of perpendicular lines are negative reciprocals of each other.
These are the best ways to determine if a triangle is a right triangle with one 90-degree angle.