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dolphi86 [110]
3 years ago
10

In the xy -coordinate plane, the coordinates of point s are (-2,-6), and coordinates of point T are (18,9). Point Q lies on line

segment ST so that the ratio of the distance from point S to point Q to the distance from point g to point T is 2 to 3. What are the coordinates of point Q?
Mathematics
1 answer:
ira [324]3 years ago
5 0

Answer:

(6,0)

Step-by-step explanation:

The coordinates of the points dividing the line segment in ratio m:n can be calculated as:

(\frac{mx_{2}+nx_{1}}{m+n} ,\frac{my_{2}+ny_{1}}{m+n} )

Here x1, y1 are the coordinates of first point S (-2, -6) and x2, y2 are the coordinates of second point T(18, 9).

In this case m will be 2 and n will be 3 as the ratio is 2:3

Using all these values we can find the coordinates of point Q

( \frac{2(18)+3(-2)}{2+3},\frac{2(9)+3(-6)}{2+3} )\\\\ = (\frac{30}{5} ,\frac{0}{5} )\\\\ =(6,0)

Thus, the coordinates of point Q which divides the line segment ST in ratio of 2:3 are (6,0)

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