MATH SOLVE

5 months ago

Q:
# given the points M (-3,-4) and T (5,0), find the coordinates of the point Q on direct line segment MT that partitions MT in the ratio 2:3. Write the coordinates of the point Q in decimal form.

Accepted Solution

A:

vector MT, or the change from x1 to x2 and y1 to y2 is expressed as

[tex](5 - ( - 3))i + (0 - ( - 4))j \\ = 8i + 4j[/tex]

no worries if you are unfamiliar with vector notation which is the the I and j there. it just shows that from point m to point t, x increases by 8 and y increases by 4. now find

[tex] \frac{2}{3} 8 \: \: \: \: and \: \: \: \: \frac{2}{3} 4[/tex]

that is

[tex] \frac{16}{3} and \frac{8}{3} [/tex]

add the 16/3 to the original value of x and 8/3 to the original value of y. the original value is point m.

now your point q should equal

[tex]( \frac{16}{3} + ( - 3))x \: \: and \: \: ( \frac{8}{3} + ( - 4))y[/tex]

[tex](5 - ( - 3))i + (0 - ( - 4))j \\ = 8i + 4j[/tex]

no worries if you are unfamiliar with vector notation which is the the I and j there. it just shows that from point m to point t, x increases by 8 and y increases by 4. now find

[tex] \frac{2}{3} 8 \: \: \: \: and \: \: \: \: \frac{2}{3} 4[/tex]

that is

[tex] \frac{16}{3} and \frac{8}{3} [/tex]

add the 16/3 to the original value of x and 8/3 to the original value of y. the original value is point m.

now your point q should equal

[tex]( \frac{16}{3} + ( - 3))x \: \: and \: \: ( \frac{8}{3} + ( - 4))y[/tex]