Question

Given MP with M(-12,-5) and P(9,-12), if N lies on MP such that the ratio

(a) 1:2
(b) 2:1
(c) -2:1
(d) 1:-2

Answer 1

To find the coordinates of point N that lies on line segment MP with given endpoints and ratios, the section formula is applied. Ratios like -2:1 or 1:-2 are generally not conventional, unless specified in the context. The section formula helps determine N's location on the segment.

Step-by-step explanation:

The question is asking for the coordinates of the point N that lies on line segment MP, given two end points M(-12, -5) and P(9, -12), and specific ratios that define how N divides MP. To find the coordinates of the point N for each ratio, we use the section formula:

• For the ratio 1:2, the coordinates of N can be found using the formula (mx2 + nx1)/(m + n), (my2 + ny1)/(m + n) where M(x1, y1), P(x2, y2), m=1, n=2.
• For the ratio 2:1, similar calculations would be performed with m=2, n=1.
• Ratios with negative values such as -2:1 or 1:-2 are not conventional for ratios of division in a line segment, so these can typically be ignored unless working with directed line segments or specific contexts where negative ratios are meaningful.

All calculations should result in the coordinates of point N, which will reveal how it divides the line segment MP according to the given ratios.