Point A is at #(9 ,-2 )# and point B is at #(2 ,4 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

Answer 1

The distance has changed by #abs(bar(AB) - bar(A^’B)) = abs(sqrt(13)-sqrt(45))#

Consider the point #A(9,-2)#, a rotation by #pi# will put A at #A^’(9,2 )#. Point B is at #B(2,4)# we need to calculate the distance of #bar(AB)# and #bar(A^’B)# and compare the difference: Distance Formula: #d = sqrt((x_2-x_1)^2 +(y_2-y_1)^2)# #bar(AB) = sqrt((9-2)^2 +(-2-4)^2) = 49-36# #bar(AB) = sqrt (13)# #bar(A^’B) = sqrt((9-2)^2 +(2-4)^2)=49-4# #bar(AB) = sqrt (45)# The length of #bar(AB)# changed by #abs(sqrt(13)-sqrt(45))#
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Answer 2

The new coordinates of point A after rotating π radians clockwise about the origin are (-9, 2). The distance between points A and B remains unchanged after the rotation. Therefore, the distance between the original point A and point B is equal to the distance between the rotated point A and point B. The distance between points A and B can be calculated using the distance formula: (d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}). Substituting the coordinates of the points into the formula, the distance between points A and B is found to be (d = \sqrt{(2 - 9)^2 + (4 - (-2))^2} = \sqrt{(-7)^2 + (6)^2} = \sqrt{49 + 36} = \sqrt{85}). Therefore, the distance between points A and B remains (\sqrt{85}) units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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