Question

The distance from point A(x, 1) to point B(0, 7) is equal to 10. Calculate the value of the abscissa x.​

Answer 1

• The abscissa is one of x = 8 or x = - 8

-------------------------------------------

Use the distance formula:

• 
  `d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Given:

• x₁ = x, x₂ = 0, y₁ = 1 , y₂ = 7, d = 10

Substitute these values and solve for x:

• 
  `10=√((0-x)^2+(7-1)^2)`
• 
  `10=√(x^2+6^2)`
• 
  `10^2=x^2+36`
• 
  `100 = x^2+36`
• 
  `x^2=64`
• 
  `x=√(64)`
• 
  `x=8,\ or \ x = -8`

Answer 2

Point distance :

After performing the calculations, we conclude that the value of the abscissa "x" is 8.

To find the answer, let's use the formula to calculate the distance between two points:

`\bold{d_(AB)^2=(x_b-x_a)^2+(y_b-y_a)}`

Substituting the values in the formula, we get: