If line A contains Q(5,1) and is parallel to line MN with M(-2,4) and N(2,1), which ordered pair would be on the perpendicular t

The options you provided are unclear to me, so I will respond in general terms: to determine if a point (ordered pair) lies on a line, you need to substitute the x-value from that pair into the line's equation and check if the resulting y-value matches the y-value of the ordered pair. For example, if your line is y = 4/3x + 1/3, we can check if (0, 0) and (2, 3) fit this line. We find that y = 4/3·0 + 1/3 gives us 1/3, which does not equal 0, indicating (0, 0) is not on the line. For (2, 3), substituting yields y = 4/3·2 + 1/3 = 3, meaning (2, 3) is on the line.

The coordinates -1, -1 lie on the line defined by the equation y = 4/3x + 1/3. The following explains the nature of straight-line equations in the Cartesian plane. The general formula is given by y = mx + c, where m represents the slope (gradient) and c is the y-intercept. The gradient (m) can be calculated as Δy / Δx. Important properties of lines include the gradient of a line parallel to the x-axis being 0, while that parallel to the y-axis is undefined. For two parallel lines, their gradients will match, and in the case of two perpendicular lines, the product of their gradients equals -1.