Estudo Do Plano Cartesiano

At point P(3,7), the x-coordinate is 4 units less than the y-coordinate. This means that the x-coordinate is 3-4 = -1, and the y-coordinate is 7. Therefore, the statement is true.

The statement is true because it states that point A(0,7) should be marked on the 7 of the y-axis. This means that the x-coordinate of point A is 0 and the y-coordinate is 7. Therefore, the point should be plotted on the y-axis at the height of 7 units.

No ponto P(4,8), a abscissa é o dobro da ordenada. No entanto, neste caso, a abscissa é 4 e a ordenada é 8, o que não confirma a afirmação de que a abscissa é o dobro da ordenada. Portanto, a resposta correta é "Falso".

The statement is true because the point A(5,0) has a x-coordinate of 5, which means it lies on the 5 of the x-axis.

The given equation y = -2x + 4 represents a linear relationship between the variables x and y. To find the value of y when x = 1, we substitute x = 1 into the equation: y = -2(1) + 4. Simplifying this expression gives y = 2. Therefore, when x = 1, y = 2.

The correct answer is (-2,4) because when we substitute x = -2 into the equation y = x^2, we get y = (-2)^2 = 4. This point satisfies the given relationship between the abscissa and the ordinate.

The given answer, 2, 3, 1, 4, and 2, represents the quadrants to which the points A(-1,1), B(-2,-3), C(1,2), D(3,-1), and E(-3,2) respectively belong. To determine the quadrant of a point, we consider the signs of its x-coordinate and y-coordinate. In the given answer, the point A has a negative x-coordinate and a positive y-coordinate, which places it in the second quadrant. The point B has both negative x-coordinate and y-coordinate, placing it in the third quadrant. The point C has positive x-coordinate and y-coordinate, placing it in the first quadrant. The point D has positive x-coordinate and negative y-coordinate, placing it in the fourth quadrant. The point E has a negative x-coordinate and a positive y-coordinate, placing it in the second quadrant again.

The distance between two points in a coordinate plane can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2]. In this case, the x-coordinates of points A and B are -1 and 3 respectively, and the y-coordinates are 2 for both points. Plugging these values into the distance formula gives us the square root of [(3 - (-1))^2 + (2 - 2)^2], which simplifies to the square root of (4^2 + 0^2), or the square root of 16. The square root of 16 is 4, so the distance between points A and B is 4 units. Therefore, the given answer of 5 is incorrect.

The given equation y = -2x + 4 represents a linear relationship between the variables x and y. To find the value of y when x = 4, we substitute x = 4 into the equation. Thus, y = -2(4) + 4 = -8 + 4 = -4. Therefore, the value of y when x = 4 is -4.

If the relationship between variables x and y is given by y = -2x + 4, and we are told that y = 10, we can substitute y with 10 in the equation and solve for x. By substituting, we get 10 = -2x + 4. Solving this equation, we subtract 4 from both sides to isolate -2x, resulting in 6 = -2x. Dividing both sides by -2, we find that x = -3. Therefore, if y is equal to 10, then x is equal to -3.

The given equation is y = -2x + 4. If y = 4, then we can substitute this value into the equation to find x. So, 4 = -2x + 4. By subtracting 4 from both sides of the equation, we get 0 = -2x. Dividing both sides by -2, we find that x = 0.

The first statement is correct because any point with an abscissa (x-coordinate) of zero will lie on the y-axis.

The second statement is correct because any point with an ordinate (y-coordinate) of zero will also lie on the y-axis.

The third statement is correct because the origin, O(0,0), is the point where the x-axis and y-axis intersect.

The fourth statement is incorrect because a point in the third quadrant will have negative coordinates.

The fifth statement is correct because the coordinates (x,y) define the location of a point in the Cartesian plane.

The given answer states that the vertices of the rectangle ABCD are A(-2,1), B(-2,-2), C(2,-2), and D(2,1). It also states that the perimeter of the rectangle measures 14 units of length and that ABCD has an area of 12 square units.

The statement "As circunferências tem raios iguais" is correct because the question states that the circles have equal radii.

The statement "As coordenadas das interseções das circunferências são (0,-1) e (2,1)" is correct because the question states that these are the coordinates of the intersections of the circles.

The statement "A, B, C e D são vértices de um quadrado de 4 unidades de área" is correct because the question implies that A, B, C, and D are the centers of the circles, and if they form a square, then they are indeed vertices of a square.

The statement "Uma 3ª circunferência, com centro em D e que tangencie as outras circunferências, tem raio medindo 4" is correct because the question states that there is a third circle with center D that is tangent to the other circles, and its radius is given as 4.

The given answer is correct because it accurately identifies the statements that are true based on the given information. It states that the segment AB contains 5 points with integer coordinates, which is true as A, B, and C have natural coordinates. It also correctly states that AB intersects the y-axis at (0,1) and that (0,1) is the midpoint of AB. Additionally, it states that (0,1) is equidistant from points A, B, and C, which is true as all three points lie on the same line.