Question

Please help me id really appreciate it so much

A- (2.4, 0)
B- (0, -1)
C- (0.4,0)
D- (1, 2)

Answer 1

The distance between points A(2.00 m, -4.00 m) and B(-3.00 m, 3.00 m) is approximately 8.60 meters, and their polar coordinates are found by using the radius and arctan functions, considering the correct quadrants based on the signs of the coordinates.

Step-by-step explanation:

To find the distance between two points in the Cartesian plane, such as points A(2.00 m, -4.00 m) and B(-3.00 m, 3.00 m), we use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values:

Distance = √((-3 - 2)^2 + (3 - (-4))^2) = √(25 + 49) = √(74)

Distance is approximately 8.60 m.

For polar coordinates, we convert each point's Cartesian coordinates to polar form using the following relations:

r = √(x^2 + y^2) and θ = arctan(y/x), where r is the radius and θ is the angle from the positive x-axis.

For point A:

rA = √(2^2 + (-4)^2) = √(20)

θA = arctan(-4/2) = arctan(-2) (Assume in the correct quadrant)

For point B:

rB = √((-3)^2 + (3)^2) = √(18)

θB = arctan(3/-3) = arctan(-1) (Assume in the correct quadrant)

Remember to consider the signs of the coordinates to determine the correct quadrant for θ.

Answer 2

It’s D, the axis of symmetry (aos) is 1 and the -2 is the y coordinate to the aos which is also the minimum of the parabola