How do you find the possible values for a if the points (6,a), (5,0) has a distance of #sqrt17#?

Answer 1

To find the possible values for a, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

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

In this case, we have the points (6, a) and (5, 0), and the distance is sqrt(17). Plugging these values into the distance formula, we get:

sqrt(17) = sqrt((5 - 6)^2 + (0 - a)^2)

Simplifying the equation, we have:

17 = (5 - 6)^2 + (0 - a)^2

17 = 1 + a^2

Rearranging the equation, we get:

a^2 = 16

Taking the square root of both sides, we have:

a = ±4

Therefore, the possible values for a are 4 and -4.

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Answer 2

Julia Adams

#a=-4# or #a=4#

The distance between two points #(x_1,y_1)# and #(x_2,y_2)# is

#sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

Hence, distance between two points #(6,a)# and #(5,0)# is

#sqrt((5-6)^2+(0-a)^2)# and this should be #sqrt17#

Therefore #sqrt((5-6)^2+(0-a)^2)=sqrt17#

or #(5-6)^2+(0-a)^2=17#

i.e. #1+a^2=17#

or #a^2-16=0#

or #(a+4)(a-4)=0#

i.e. #a=-4# or #a=4#

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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.