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2 years ago

for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).

Mathematics

1 answer:

Schach [20]2 years ago

4 0

Answer:

k = 18

=========

<h2>Given</h2>

3x - ky + 7 = 0

Passing through the points (4, 3) and (5, - 3)

The value of k, if the lines are perpendicular

<h2>Solution</h2>

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

<em>standard form is ⇒ ax + by + c = 0, </em>
<em>slope - intercept form is ⇒ y = mx + b, where m is the slope</em>

3x - ky + 7 = 0
ky = 3x + 7
y = (3/k)x + 7/k

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6

We have both the slopes now. Find their product:

(3/k)*(- 6) = - 1
- 18/k = - 1
k = 18

So when k is 18, the lines are perpendicular.

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Step-by-step explanation:

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For this exercise you need to use the following formula, which can be used for calculate the distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In this case, you need to find distance, in yards, between the pine tree and the apple tree in the park.

You know that pine tree is located at the point (-2.4, 5) and the apple tree is located at the point (7.8, 5).

So, you can say that:

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3 years ago

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Answer:

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