Point B has coordinates (4,1). The x-coordinate of point A is -4. The distance between point A and point B is 10 units. What are the possible coordinates of point A?

Question

asked Oct 23, 2022 111k views

1 Answer

Gildas · Answer 1 · 2022-10-27T21:08:59+0000

Given:

Point B has coordinates (4,1).

The x-coordinate of point A is -4.

The distance between point A and point B is 10 units.

To find:

The possible coordinates of point A.

Solution:

Let the y-coordinate of point A be y. Then the two points are A(-4,y) and B(4,1).

Distance formula:

D=√((x_2-x_1)^2+(y_2-y_1)^2)

The distance between point A and point B is 10 units.

√((4-(-4))^2+(1-y)^2)=10

Taking square on both sides, we get

(8)^2+(1-y)^2=100

(1-y)^2=100-64

(1-y)^2=36

Taking square root on both sides, we get

$(1-y)=\pm √(36)$

$-y=\pm 6-1$

$y=1\mp 6$

y=1-6 and
y=1+6

y=-5 and
y=7

Therefore, the possible coordinates of point A are either (-4,-5) or (-4,7).