Find the point, m, that is two-sevenths of the distance from a(-9, 2) to b(-2, -12)

Solution:

Given, the points a(-9, 2) and b(-2, -12)

We have to find the two-sevenths of the distance(m) between the points a to b.

Using the distance formula

Distance = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

Distance, m = \(\sqrt{(-2-(-9))^{2}+(-12-2)^{2}}\)

= \(\sqrt{(-2+9)^{2}+(-14)^{2}}\)

= \(\sqrt{(7)^{2}+(-14)^{2}}\)

= \(\sqrt{49+196}\)

= \(\sqrt{245}\)

= 15.65

Now, two-sevenths of the distance m = (2/7)m

= (2/7)15.65

= 4.47 units.

Therefore, two-sevenths of the distance m is 4.47 units.

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Find the point, m, that is two-sevenths of the distance from a(-9, 2) to b(-2, -12)

Summary:

The point, m, that is two-sevenths of the distance from a(-9, 2) to b(-2, -12) is 4.47 units.