Question

mark the statement true or false(t/f).justify your answer. the points in the plane corresponding to −2;5 and −5;2 lie on a line through the origin

Answer 1

The points (-2, 5) and (-5, 2) do not lie on a line through the origin.

Step-by-step explanation:

The statement is false. The points (-2, 5) and (-5, 2) do not lie on a line through the origin.

To determine if the points lie on a line through the origin, we can check if their coordinates satisfy the equation of a line passing through the origin, which is y = mx, where m is the slope of the line. To find the slope, we can use the formula m = (y2 - y1) / (x2 - x1). For (-2, 5) and (-5, 2), the slope is (2 - 5) / (-5 - (-2)) = -3 / -3 = 1. So, the equation of the line passing through the origin is y = x.

Substituting the points' coordinates into this equation, we have 5 = -2 and 2 = -5, which are both false. Therefore, the points (-2, 5) and (-5, 2) do not lie on a line through the origin.