Question

Find all points having an​ x-coordinate of 3 whose distance from the point(-1,-4) is 5

Answer 1

Please refer the attachment

Answer 2

SOLUTION

TO DETERMINE

All points having an x-coordinate of 3 whose distance from the point(-1,-4) is 5

FORMULA TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$ the distance between the points

$= \sf{ \sqrt{ {(x_2 -x_1 )}^{2} + {(y_2 -y_1 )}^{2} } }$

EVALUATION

Here it is given that for the required point x-coordinate = 3

Let the coordinates of the point = (3,k)

So the distance of (3,k) from the point(-1,-4) is 5

So by the given condition

$\sf{ \sqrt{ {(3 + 1)}^{2} + {(k + 4)}^{2} } = 5 }$

$\sf{ \implies \: {(3 + 1)}^{2} + {(k + 4)}^{2} = {5}^{2} }$

$\sf{ \implies \: {(4)}^{2} + {(k + 4)}^{2} = {5}^{2} }$

$\sf{ \implies \: {(k + 4)}^{2} = 25 - 16 }$

$\sf{ \implies \: {(k + 4)}^{2} = 9 }$

$\sf{ \implies \: (k + 4) = \pm \: 3 }$

k + 4 = 3 gives k = - 1

k + 4 = - 3 gives k = - 7

Hence the required coordinates of the point = (3,-1) or (3,-7)

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. the distance between the point P[-(11/3),5] and Q[-(2/3),5]is

https://brainly.in/question/14757917

2. Find the value of a, if the distance between the points A(-3 , -14) and B(a, -5) is 9 units

https://brainly.in/question/31582162