Question

Find the​ y-coordinates of the points that are 5 units away from the point left parenthesis 1 comma 3 right parenthesis that have an​ x-coordinate of negative 3 .

Answer 1

0, 6

Explanation:

To find : y-coordinates of the points that are 5 units away from the point left parenthesis 1 comma 3 right parenthesis that have an​ x-coordinate of negative 3

Given:

Point left parenthesis 1 comma 3 right parenthesis i.e point
`\left (1 ,3 \right )`

Also, point is 5 units away from the point left parenthesis 1 comma 3 right parenthesis such that it's x - coordinate is negative 3 i.e, - 3

Distance between points
`\left ( -3,y \right )\, \,\left (1 ,3 \right )` is 5 units,

`√((1+3)^2+(3-y)^2)=5\\√(16+9+y^2-6y)=5\\√(25+y^2-6y)=5\\y^2-6y+25=25\\y^2-6y=0\\y(y-6)=0\\y=0\,,\,6`

{ as distance between points
`\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )` is equal to
`√(\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2)` }

Answer 2

The x-distance to the points of interest is 1 - (-3) = 4. The straight-line distance is 5, so the y-distance can be computed using the Pythagorean theorem as
y-distance = √(5²-4²) = √9 = 3

Your points have y-coordinates of 3±3, or 0 and 6.