138k views
0 votes
Suppose point A is located at (1, 3) on a coordinate plane. If AB is 10 and the x-coordinate of point B is 9, explain how to use the Distance Formula to find the y-coordinate of point B.

2 Answers

7 votes

Final answer:

To find the y-coordinate of point B, you can use the Distance Formula. By substituting the given values into the formula and simplifying, you find that the y-coordinate of point B can be either 3 + √19 or 3 - √19.

Step-by-step explanation:

To find the y-coordinate of point B, we can use the Distance Formula. The formula is:


d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)

Given that point A is located at (1, 3) and the x-coordinate of point B is 9, we can substitute these values into the formula:


d = \sqrt{((9 - 1)^2 + (y2 - 3)^2)

Since AB is 10, we can replace d with 10 and simplify:


10 = \sqrt{((9 - 1)^2 + (y2 - 3)^2)

Squaring both sides of the equation:


100 = (9 - 1)^2 + (y2 - 3)^2


81 + (y2 - 3)^2 = 100


(y2 - 3)^2 = 100 - 81


(y2 - 3)^2 = 19


y2 - 3 = +/-\sqrt{19

So, the y-coordinate of point B can be either 3 + √19 or 3 - √19.

User Injecto
by
8.0k points
12 votes

Answer:

y =9

Step-by-step explanation:

you know the distance is 10 and some of the x,y points. so start filling what you know into the distance formula

10= √((9-1)^2 + (y-3)^2 )

square both sides to get ride of the square root

100 = 64 + (y-3)^2

36 = (y-3)^2

6 = y-3

y = 9

double check by using 9 for Y and you'll see it works.

User Chema
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.