Algebra - How to graph a point

The length of line segment $\overline{AB}$ is 12 units. If point A is located at , what is a possible location for point B?

$(14, 5+2\sqrt{11})$

$(2\sqrt{11}, 10)$

$(4+2\sqrt{22}, 15)$

Explanation

To answer this question, we will have to manipulate the distance formula:

$d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}$

To get rid of the square root, we can square both sides:

$d^{2}=(x_{1}-x_{2})^{2}}+(y_{1}-y_{2})^{2}}$

and plug in the information given in the question.

$12^{2}=(4-x_{2})^{2}}+(5-y_{2})^{2}}$

$144=(4-x_{2})^{2}}+(5-y_{2})^{2}}$

At this point we can simply plug in the possible values to determine which combination of coordinates will make the equation above true.

$144=(4-14)^{2}}+(5-(5+2{\sqrt{11}}))^{2}}$ $=(-10)^{2}+(2\sqrt{11})^{2}=100+44=144$

Thus the correct coordinate is,

$(14, 5+2\sqrt{11})$ .

Graph the following 4 points. They will be displayed as (x,y) pairs.

(A) $\left ( 1,3\right )$

(B) $\left ( 2,-2\right )$

(D) $\left ( -2,-3\right )$

Explanation

To graph these points we just need to remember that the first number is the x value and the second number is the y value. For (A) we have (1,3). So we move one tick over on the positive x-axis. Then from there we move up to the third tick on the y axis:

If the value is negative we must move in the other direction. So, for all 4 points,

All2

Which image depicts the point ?

Question_8-_correct

Question_8-_incorrect_1

Question_8-_incorrect_3

Explanation

The first number, indicates how far the point is positioned to the left or right of the origin. Because the number is negative, the point is three units to the LEFT of the origin. The second number indicates how far the point is postioned up or down from the origin. Because the number is positive, the point is located four units above the origin.

What are the coordinates of the point on the given graph?

Graphin a point

Explanation

When trying to determine coordinates of a point you need to look at the value of x first (how many units left or right the point is, then the y-value (how many up or down it is).

When you look at this point you see that it is moved right 2 units and up 1.

So your coordinates are:

How to graph a point

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