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Part 1
Point B has coordinates ​(5​,1​). The​ x-coordinate of point A is −3. The distance between point A and point B is 10 units. What are the possible coordinates of point​ A?



Answer :

MrRoyal

The possible coordinates of the point​ A is (-3, -5) and  (-3, 7)

How the coordinates of point​ A can be calculated?

The given parameters are:

  • Point B = (5, 1)
  • Distance between the two points, D = 10 units
  • x-coordinate of point A = −3 i.e. A = (-3, y)

The distance between any two points is calculated as

D = √[(x₁ - x₂)² + (y₁ - y₂)²]

Substitute the known values in the above equation

So, we have

10 = √[(-3 - 5)² + (y - 1)²]

Evaluate

100 = 64 + (y - 1)²

Evaluate the like terms

(y - 1)² = 36

Take the square roots

y - 1 = ±6

This gives

y = 1 ± 6

So, we have

y = -5 and 7

Hence, the value of point​ A are (-3, -5) and  (-3, 7)

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