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aniked [119]
3 years ago
12

Find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).

Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
4 0
Since M divides segment AB into a ratio of 5:2, we can say that M is 5/(5+2) of the length of AB. Therefore 5/7 × AB.
distance of AB = d
5/7×(x2 - x1) for the x and 5/7×(y2 - y1) for the y
5/7×(8 - 1) = 5/7 (7) = 5 for the x
and 5/7×(16 - 2) = 5/7 (14) = 10 for the y
But remember the line AB starts at A (1, 2),
so add 1 to the x: 5+1 = 6
and add 2 to the y: 10+2 = 12
Therefore the point M lies exactly at...
A) (6, 12)


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Answer:

The y-intercept is (0,-26)

Step-by-step explanation:

Given two points P(a,b) and Q(c,d), the line that passes for both points can be found with the expression

\displaystyle y-b=\frac{d-b}{c-a}(x-a)

We'll take the first two points P(34,-52) and Q(51,-65) to find

y=-\frac{13}{17}(x-34)-52\\ \\y=-\frac{13}{17}x-26

Let's verify if the third point is on the line:

y=-\frac{13}{17}68-26=-52-26=-78

It belongs to the line. To find the y-intercept of the line, we set x to 0

y=-\frac{13}{17}(0)-26=-26

The y-intercept is (0,-26)

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