Question

A point H on a segment with endpoints B(3, -1) and Z(12, 5) partitions the segment in a 5:1 ratio. Find H. I suck at the ratios of a line :/

Answer 1

there is a formula you can use
(x ,y) = (x1 + k(x2-x1)) , ( y1 + k(y2 - y1))

where k = 5 / (5 + 1)

Answer 2

Sketching this situation would very likely help you to estimate what the correct answer is. Would you try out the Draw utility for this purpose?

Plot the 2 giv en points and then draw a line connecting them.

How long is this line? Use the Pythagorean Theorem or distance formula to answer that question.

Answer 3

So k is the ratio?

Answer 4

And the distance of the line is 10.82

Answer 5

I dont think i did it roght because i got 34.5 for x and -1 for y im gonna try again but i dont know

Answer 6

I redid it and got 9 and 2/3 for x

Answer 7

And i cant just estimate the right answer i have to write it in sentences with an explanation :/

Answer 8

@mathmale

Answer 9

@welshfella

Answer 10

x1 = 3 , y1 = -1
x2 = 12 , y2 = 5

Answer 11

k = 5/6

so we have
(3 + (5/6)( 12-3) , (-1 + (5/6)(5 -(-1))

Answer 12

Okay i see where i messed up now so H should be (10.5, 4) right?

Answer 13

yes