A(7, -9) and B(-2, -4) are points on the coordinate plane.(3 points)
1) What is the distance between A and B?
To find the distance between two points on the coordinate plane, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of A and B:
Distance = √((-2 - 7)^2 + (-4 - (-9))^2)
= √((-9)^2 + (5)^2)
= √(81 + 25)
= √106
Therefore, the distance between A and B is √106.
2) What is the midpoint of the line segment AB?
To find the midpoint of the line segment AB, we can use the midpoint formula:
Midpoint = ((x1 + x2)/2 , (y1 + y2)/2)
Plugging in the coordinates of A and B:
Midpoint = ((7 + (-2))/2 , (-9 + (-4))/2)
= (5/2 , -13/2)
Therefore, the midpoint of the line segment AB is (5/2 , -13/2).
3) What is the slope of the line passing through points A and B?
To find the slope of a line passing through two points, we can use the slope formula:
Slope = (y2 - y1)/(x2 - x1)
Plugging in the coordinates of A and B:
Slope = (-4 - (-9))/(-2 - 7)
= (5)/(-9)
= -5/9
Therefore, the slope of the line passing through points A and B is -5/9.