The point (3,a) is 5 units from the point (7,9), Find all the values of a

Question

This is for my geometry class, I need a step by step answer because I’m having trouble understanding it

Answer 1

5 = sqrt ( (3-7)^2 + (a-9)^2 )

= sqrt( (-4)^2 + (a-9)^2 )

= sqrt( 16 + (a-9)^2 )

= sqrt ( 16 + a^2 - 18a + 81)

= sqrt( a^2 - 18a + 97)

so 25 = a^2 - 18a + 97

0 = a^2 - 18a + 72

0 = (a - 12)(a - 6)

a = 12 or a=6

so there are two such points that

are 5 units from (7,9).

They are (3,12) and (3,6)

Answer 2

Edisa

Draw a picture, with the point (7,9) and the line x=3.

You need to find the points on that line distance 5 from (7,9).

The horizontal distance from (7,9) to x=3 is 4 units. that means using pythagoras the distance from (3,4) to (3,a) must be 3 units so a= 6 or 1.

Mike

Answer 3

distance squared = sum of differences between x & y coordinates

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

5^2 = 4^2 + (9-a)^2

25= 16 + 81 -18a + a^2

a^2 -18a + 72 = 0

a^2 -18a + 81 = -72+81 = 9

(a-9)^2 = 9

a-9 = + or - 3

a = 9+3 or 9-3

a= 12 or 6