In the figure, a line through points C and D will represent the linear relationship between those two points in a coordinate system. This line can be described using the slope-intercept form if the coordinates of points C and D are known. Additionally, the line can be used to predict values or analyze trends related to the data represented by those points.
A line will have an undefined slope if it is vertical, which occurs when both points have the same x-coordinate. In this case, points A (4, 4) and C (4, -4) share the same x-coordinate of 4. Therefore, a line going through points A and C would have an undefined slope.
Three noncollinear points A, B, and C determine exactly three lines. Each pair of points can be connected to form a line: line AB between points A and B, line AC between points A and C, and line BC between points B and C. Thus, the total number of lines determined by points A, B, and C is three.
The graph of ax + by = c is a straight line going through the points (0, c/b) and (c/a, 0).
Three noncollinear points ( A ), ( B ), and ( C ) determine exactly three lines: line ( AB ), line ( BC ), and line ( AC ). Each pair of points defines a unique line, and since the points are noncollinear, no two lines coincide. Thus, the total number of lines determined by points ( A ), ( B ), and ( C ) is three.
Collinear.
A line will have an undefined slope if it is vertical, which occurs when both points have the same x-coordinate. In this case, points A (4, 4) and C (4, -4) share the same x-coordinate of 4. Therefore, a line going through points A and C would have an undefined slope.
Three noncollinear points A, B, and C determine exactly three lines. Each pair of points can be connected to form a line: line AB between points A and B, line AC between points A and C, and line BC between points B and C. Thus, the total number of lines determined by points A, B, and C is three.
The graph of ax + by = c is a straight line going through the points (0, c/b) and (c/a, 0).
This has infinite no. of solutions.
They are collinear points that lie on the same line
In the given scenario, points A, B, C, and D are reflected across a line or point to coincide with points G, J, I, and H, respectively. This reflection implies that each original point and its corresponding reflected point are equidistant from the line of reflection. Therefore, the positions of points A, B, C, and D are symmetrically opposite to points G, J, I, and H concerning the line of reflection. This geometric relationship highlights the properties of reflection in a coordinate plane.
Three noncollinear points ( A ), ( B ), and ( C ) determine exactly three lines: line ( AB ), line ( BC ), and line ( AC ). Each pair of points defines a unique line, and since the points are noncollinear, no two lines coincide. Thus, the total number of lines determined by points ( A ), ( B ), and ( C ) is three.
Collinear.
The general form of the equation of a line is typically expressed as ( Ax + By + C = 0 ), where ( A ), ( B ), and ( C ) are constants. To determine the specific equation for a given line, you would need the slope and a point on the line or two points through which the line passes. From this information, you can calculate the coefficients ( A ), ( B ), and ( C ) accordingly.
Two points determine a unique line. Therefore, there are infinitely many circles that can pass through two given points. This is because a circle can be defined by its center, which can lie anywhere along the perpendicular bisector of the line segment connecting the two points.
This depends on what the points are for B, and C.
gradient = (-2-5) / (2-1) = -7 hence y = -7x + C Since a point on the line is (1,5) 5 = -7 + C from which we have C = 12 The equation is y = 12 - 7x