Question

Find the coordinates of points whose abscissa is −4 and which are at a distance of 15 units from (5, −9).

Answer 1

Coordinates of points whose abscissa = −4 and which are at a distance of 15 units from the point (5,−9).

Step 1: Let the required point be

P(−4, y)

Step 2: Apply the distance formula

`"Distance" = sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`

P(−4, y)

Q(5,−9)

Distance = 15

`sqrt((5 − (−4))^2 + (−9 − y)^2) = 15`

`sqrt((9)^2 + (y + 9)^2) = 15`

`sqrt(81 + (y + 9)^2) = 15`

Step 3: Square both sides

81 + (y + 9)² = 225

(y + 9)² = 225 − 81

`(y + 9)^2 = 144`

Step 4: Solve for y

y + 9 = ± 12

y + 9 = 12

y = 3

y + 9 = −12

y = −21

The required point are (−4, 3) and (−4, −21)