anonymous
  • anonymous
Find the distance between the point (-3,-4), and the line 2y =-3x+6
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
do you know how to find a perpendicular line?
anonymous
  • anonymous
NO
ybarrap
  • ybarrap
If you have a line with a slope of -3/2 then the slope of a line perpendicular to it will have a negative reciprocal of it, that is 2/3. But you want this perpendicular line to go through the point (-3,4) so we need to use the new perpendicular equation y= (2/3) x + b to find the y-intercept, b: $$ 4=(2/3)(-3)+b $$ From which you can now get b. This perpendicular line intersects the original line when both of these equations are equal $$ (2/3)x+b=(-3/2)x+6 $$ Solve for x to find where on the x-axis these lines intersect and then plug in to either equation to find y. This gives you where the two points intersect. But why do we want to find this perpendicular line that goes through the given point? We do this because the shortest distance between a point and a line is THE line that is perpendicular to the line and goes through the given point like this: |dw:1433096077926:dw| Once you have this point, where the perpendicular intersects the original line. Use the coordinates to find the distance, d: $$ d=\sqrt{(x_1-x_2)^2+(y_1+y_2)^2} $$ Where \(x_1=-3,y_1=-4\), the point given, that is (-3,-4), and \((x_2,y_2)\) is the point where the perpendicular line intersects the original line. Doe this make sense?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

ybarrap
  • ybarrap
|dw:1433096543445:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.