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<h4>Identifying Coordinates of a Point on a Graph</h4>
<p dir="ltr">In the rectangular coordinate system, every point is represented by an <em>ordered pair</em>. The first number in the ordered pair is the <strong>\( x \)</strong><strong>-coordinate</strong> of the point, and the second number is the <strong><em>\( y \)</em>-coordinate</strong> of the point. An ordered pair, \( (x, y) \), gives the coordinates of a point in a rectangular coordinate system. The first number is the \(x\)-coordinate. The second number is the \(y\)-coordinate. The phrase “ordered pair” means the order is important. What is the ordered pair of the point where the axes cross? At that point, both coordinates are zero, so its ordered pair is \( (0,0) \). The point \( (0,0) \) has a special name. It is called the origin.</p>
<p dir="ltr">We use the coordinates to locate a point on the \( xy \)-plane. Let’s plot the point \( (1,3) \) as an example. First, locate 1 on the \( x \)-axis and lightly sketch a vertical line through \( x=1 \). Then, locate 3 on the \(y\)-axis and sketch a horizontal line through \( y=3 \). Now, find the point where these two lines meet—that is the point with coordinates \( (1,3) \).</p>
<p dir="ltr"><strong><img alt="The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the \(x\)-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the \(x\)-axis, the other parallel to the \(y\)-axis, meet perpendicularly at 1, 3. The dotted line parallel to the \(x\)-axis intercepts the \(y\)-axis at 3. The dotted line parallel to the \(y\)-axis intercepts the \(x\)-axis at 1." height="286" src="https://k12.openstax.org/contents/raise/resources/002978e30235019b71aa8e63d74da3907a4e62fb" width="280"></strong><br></p>
<p>Notice that the vertical line through \( x = 1 \) and the horizontal line through \( y = 3 \) are not part of the graph. We just used them to help us locate the point \( (1,3) \).</p>
<p>In algebra, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the \( x \)-coordinate of a point on a graph, read the number on the \( x \)-axis directly above or below the point. To identify the \( y \)-coordinate of a point, read the number on the \(y\)-axis directly to the left or right of the point. Remember, when you write the ordered pair, use the correct order, \( (x,y) \).</p>
<h4>Try It: Identifying Coordinates of a Point on a Graph</h4>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="eventShow1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<p>Name the ordered pair of each point shown in the rectangular coordinate system.</p>
<p><strong><img height="309" src="https://k12.openstax.org/contents/raise/resources/1b68e3cfdc870cc7d8acea7f5571a72a1a67a482" width="301"></strong></p>
<p><span><span>Write down your answers, and then select the <strong>solution</strong> button to compare your work.</span><br></span></p>
</div>
<div class="os-raise-ib-cta-prompt">
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="eventShow1">
<p><span><span>Here is the explanation for each ordered pair:</span></span></p>
<p><span><strong>Point \( A \)</strong> is above \( -3 \) on the \(x\)-axis, so the \(x\)-coordinate of the point is \( -3 \).</span></p>
<ul>
<li><span>The point is to the left of \( 3 \) on the \(y\)-axis, so the \(y\)-coordinate of the point is \( 3 \).</span></li>
<li><span>The coordinates of the point are \( (-3,3) \)</span></li>
</ul>
<p><span><strong>Point \( B \)</strong> is below \( -1 \) on the \(x\)-axis, so the \( x \)-coordinate of the point is \( -1 \). The point is to the left of \( -3 \) on the \(y\)-axis, so the \(y\)-coordinate of the point is \( -3 \).</span></p>
<ul>
<li><span>The coordinates of the point are \( (-1,-3) \).</span></li>
</ul>
<p><span><strong>Point \( C \) </strong>is above \( 2 \) on the \(x\)-axis, so the \(x\)-coordinate of the point is \( 2 \).</span></p>
<ul>
<li><span>The point is to the right of \( 4 \) on the \(y\)-axis, so the \(y\)-coordinate of the point is \( 4 \).</span></li>
<li><span>The coordinates of the point are \( (2,4) \).</span></li>
</ul>
<p><span><strong>Point \( D \)</strong> is below \( 4 \) on the \(x\)-axis, so the \(x\)-coordinate of the point is \( 4 \).</span></p>
<ul>
<li><span>The point is to the right of \( -4 \) on the \(y\)-axis, so the \(y\)-coordinate of the point is \( -4 \).</span></li>
<li><span>The coordinates of the point are \( (4,-4) \).</span></li>
</ul>
<p><span><strong>Point \( E \) </strong>is on the \(y\)-axis at \( y = -2 \). The coordinates of point E are \( (0,-2) \).</span></p>
<p><span><strong>Point \( F \) </strong>is on the \(x\)-axis at \( x = 3 \). The coordinates of point F are \( (3, 0) \).</span></p>
<br>
</div>
<h4>Check Your Understanding</h4>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="222aff06-bd30-47ec-a72d-7ee622ba4888" data-retry-limit="0" data-schema-version="1.0">
<div class="os-raise-ib-pset-problem" data-content-id="15a19bbb-db56-4854-90d3-1d7213780446" data-problem-type="multiplechoice" data-solution="Point \( Z \)" data-solution-options='["Point \\( W \\)", "Point \\( Z \\)", "Point \\( X \\)", "Point \\( Y \\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>Which point has coordinates \( (–4, 3) \)?</p>
<p><img alt class="img-fluid atto_image_button_text-bottom" height="600" role="presentation" src="https://k12.openstax.org/contents/raise/resources/ba6d1ab5502ad3cda1236a3ac58e284a0c68e64f" width="650"></p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response" data-answer="Point \( W \)">
<p>Incorrect. Let’s try again a different way: The first coordinate is the \( x \)-coordinate. The \( x \)-coordinate is negative 4, so move 4 units left. The second coordinate is the \( y \)-coordinate. The \( y \)-coordinate is positive 3, so move 3 units up.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response" data-answer="Point \( X \)">
<p>Incorrect. Let’s try again a different way: The first coordinate is the \( x \)-coordinate. The \( x \)-coordinate is negative 4, so move 4 units left. The second coordinate is the \(y\)-coordinate. The \( y \)-coordinate is positive 3, so move 3 units up.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response" data-answer="Point \( Y \)">
<p dir="ltr">Incorrect. Let’s try again a different way: The \( x \)-coordinate is negative 4, so move 4 units left. The \( y \)-coordinate is positive 3, so move 3 units up.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The answer is Point \( Z \).</p>
</div>
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<div class="os-raise-ib-pset-correct-response">
<p dir="ltr">That’s correct! Check yourself: The \( x \)-coordinate is negative 4. The \( y \)-coordinate is positive 3. Move 4 units left and 3 units up to point \( Z \).</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
</div>
</div>
<h4>Videos</h4>
<p>Watch the following videos to learn more about solving different types of linear equations.</p>
<h5>Khan Academy: Points on the Coordinate Plane</h5>
<p>Watch this video to see how you can use a coordinate plane to plot points and to identify the coordinates of a point plotted on a coordinate plane. <br></p>
<p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/VhNkWdLGpmA;&rel=0" title="YouTube video player"></iframe></div>
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</p><br>