Question

Point A is at (-8,7.5) and point B is at (6,3.5).

If point M=(1-t)A+tB=(-4.5,6.5).
what is the value of t?___

Answer 1

To determine the value of t for the point M given as a linear combination of points A and B, set up two separate equations using the x and y coordinates and solve them for t.

Step-by-step explanation:

The student is asking how to find the value of t when point M is a linear combination of points A and B and is given by the equation M=(1-t)A + tB. The coordinates of point A are (-8, 7.5), point B are (6, 3.5), and point M are (-4.5, 6.5). To find the value of t, we need to set up a system of equations based on the linear combination given for the x and y coordinates separately and solve for t.

For the x-coordinate, we have: -4.5 = (1-t)(-8) + t(6)

For the y-coordinate, we have: 6.5 = (1-t)(7.5) + t(3.5)

By solving these equations, we can find the value of t that satisfies both coordinates.