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2 years ago

If another line is perpendicular to the line shown on the graph, what must be its slope

Mathematics

1 answer:

Shtirlitz [24]2 years ago

4 0

It's B

Slope is negative, the other must be positive due to m1 x m2 = - 1

m1 = -2/5

The diagram shows a gradient of -2/5. So, the

reciprocal of this valve to make - 1 is 5/2 (which is the - 2/5 flipped upside down, but positive)

-2/5 x 5/2 = - 10/10 (or - 1)

Thus, the perpendicular line to this has a gradient of 5/2.

Hope this helps!

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3 years ago

In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz

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$Point\ C = (2,-1)$

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Given

$A = (2,-6)$

$B = (10,2)$

$m:n = 5:3$

Required

Determine the coordinates of C

Since, point D divides line AB in ratio, 5 : 3;

We start by calculating the coordinates of D;

This is done as follows;

$D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

$(x_1,y_1) = (2,6)$

$(x_2,y_2) = (10,2)$

$m:n = 5:3$

$D(x,y) = (\frac{5 * 10 + 3 * 2}{5+3},\frac{5 * 2 + 3 * -6}{5+3})$

$D(x,y) = (\frac{50 + 6}{8},\frac{10 - 18}{8})$

$D(x,y) = (\frac{56}{8},\frac{-8}{8})$

$D(x,y) = (7},-1)$

Since AC is vertical

Then, Point C has the same x coordinate as A

$x-coordinate = 2$

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Since CD is horizontal

Then, Point C has the same y coordinate as D

$y-coordinate = -1$

Hence,

$Point\ C = (2,-1)$

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