Answer:
A = (-1,5) or (-1,-3)
Step-by-step explanation:
A = (-1,y) B = (2,1)
(Distance from A to B) = √[(-1-2)² + (y-1)²] = 5
=√[9 + y² - 2y + 1] = 5
Squaring on both sides
= y² - 2y + 10 = 25
=y² - 2y -15 = 0
= (y-5)(y+3) = 0
y = 5 or -3
Therefore, A = (-1,5) or (-1,-3)
Answer:
(-1, 5)
(-1, -3)
Step-by-step explanation:
Given that coordinates of point B = (2,1) this means, x2 = 2 & y2 = 1.
The x coordinate of point A = -1
D = 5 units
Let's use the equation for distance between points, it is expressed as:
[tex] D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} [/tex]
[tex] 5 = \sqrt{(-1-2)^2 + (a-1)^2} [/tex]
Solving further, let's square both sides,
[tex] 5^2 = [\sqrt{(-1-2)^2 + (a-1)^2}]^2[/tex]
[tex] 25 = (-1-2)^2 + (a-1)^2 [/tex]
[tex] 25 = 9 + (a-1)^2 [/tex]
Solving further, we have:
[tex] 25 - 9 = (a-1)^2 [/tex]
[tex] 16 = (a-1)^2 [/tex]
[tex] +/- \sqrt{16} = a-1 [/tex]
[tex] +/-4 = a - 1 [/tex]
For the possible values, we have:
[tex] a = 4+1 = 5 [/tex]
[tex] a = - 4 + 1 = -3[/tex]
Therefore, the possible coordinates of point A are:
(-1, 5)
(-1, -3)
