Example Question - coordinate grid
Here are examples of questions we've helped users solve.
Identifying a Point on the Y-Axis of a Coordinate Grid
<p>The y-axis on a coordinate grid is represented by the line where the x-coordinate is 0. Therefore, we are looking for a point where the first number (x-coordinate) is 0.</p> <p>Looking at the options given:</p> <p>\((0, 7)\) - This point has an x-coordinate of 0 and a y-coordinate of 7, so this point lies on the y-axis.</p> <p>\((7, 1)\) - This point has an x-coordinate of 7, so it does not lie on the y-axis.</p> <p>\((1, 7)\) - This point has an x-coordinate of 1, so it does not lie on the y-axis.</p> <p>\((7, 0)\) - This point lies on the x-axis, not the y-axis, because the y-coordinate is 0.</p> <p>Thus, the correct answer is \((0, 7)\).</p>
Determining Coordinates of Madrid on a Grid
<p>Para encontrar las coordenadas de Madrid en la gráfica proporcionada, buscamos la intersección de la posición horizontal (eje x) y la posición vertical (eje y) de la ciudad de Madrid.</p> <p>La posición horizontal de Madrid es 2 en el eje x.</p> <p>La posición vertical de Madrid corresponde a 4 en el eje y.</p> <p>Por lo tanto, la ubicación de Madrid como un par ordenado \((x, y)\) es \((2, 4)\).</p>
Graphing a Right Triangle and Calculating Distance
The provided image shows a coordinate grid with the task to graph a right triangle with two points given: (5,2) and (2,-2), with these points forming the hypotenuse. To graph the right triangle, the third point should form a right angle with the given points. To find the third point, you can keep either the x-coordinate (5) the same and change the y-coordinate to -2, or keep the y-coordinate (2) the same and change the x-coordinate to 2. This will create a right angle at the third point. Let's use the first option and have the third point be (5, -2). Now to find the distance between the two points (5,2) and (2,-2) using the Pythagorean theorem, you calculate the lengths of the other two sides of the triangle and then apply the theorem a^2 + b^2 = c^2. The length of the triangle's side that lies along the x-axis (horizontal side) is the difference between the x-coordinates of the two points: |5 - 2| = 3. The length of the side that lies along the y-axis (vertical side) is the difference between the y-coordinates of the two points: |2 - (-2)| = |2 + 2| = 4. Now plug these values into the Pythagorean theorem to find the hypotenuse: a^2 + b^2 = c^2 3^2 + 4^2 = c^2 9 + 16 = c^2 25 = c^2 c = √25 c = 5 Therefore, the distance between the two points (5,2) and (2,-2) is 5 units.
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