Question

given two point A(-6,7) and B(1, -2) on the XOY plane, find the distance between A and B and what is the angle that the line AB makes with the X-axis?​

Answer 1

The distance between points A(-6,7) and B(1,-2) is approximately 11.4 units. The angle that the line AB makes with the X-axis is approximately -51.34°.

Step-by-step explanation:

To find the distance between points A(-6,7) and B(1,-2), we can use the distance formula, which is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates, we have:

d = sqrt((1 - (-6))^2 + ((-2) - 7)^2)

d = sqrt(7^2 + (-9)^2)

d = sqrt(49 + 81)

d = sqrt(130)

d ≈ 11.4 units

To find the angle that the line AB makes with the X-axis, we can use the tangent of the angle. The tangent of an angle is given by:

tan(theta) = (y2 - y1) / (x2 - x1)

Substituting the coordinates, we have:

tan(theta) = (-2 - 7) / (1 - (-6))

tan(theta) = (-9) / 7

Using the inverse tangent function, we can find theta:

theta = arctan((-9) / 7)

theta ≈ -51.34° (rounded to 2 decimal places)

Answer 2

AB = 11.4

the angle that the line AB makes with the X-axis: 52°

Step-by-step explanation:

AB² = AC² + CB² = 81 + 49 = 130

AB = √130 = 11.4

m∠ADE = m∠ABC

tan (∠ABC) = AC/CB = 9/7

m∠ABC = 52°

m∠ADE = 52°