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B) Find an equation for the perpendicular bisector of the segment AB. To do this You are to find an equation of a line perpendicular to the equation in Part (a) pas...

Question

B) Find an equation for the perpendicular bisector of the segment AB. To do this You are to find an equation of a line perpendicular to the equation in Part (a) passing through the midpoint of segment AB . Express your answer in slope-intercept form: Show all work

b) Find an equation for the perpendicular bisector of the segment AB. To do this You are to find an equation of a line perpendicular to the equation in Part (a) passing through the midpoint of segment AB . Express your answer in slope-intercept form: Show all work



Answers

Show that the line $y=x$ is the perpendicular bisector of the segment with endpoints $(a, b)$ and $(b, a),$ where $a \neq b .$ (Hint: Use the midpoint formula and the slope formula.)

The question on the line. So you're cool. Number equals number line using the pond Islam B Y minus Suazo, You put your aim Thames exponents extra on by this formula here, we need to fight two things. The 1st 1 with a stop came and the second thing would be the point. Eggs on y zero here. In order to do that first of from way used the first information about the questions now and it's perpendicular to that by Sigman joined with the segment here, Theo, the want you and five for socialism means standards from I'm the second here, the Eagle Jew. Why Germany's 11 they wanted by X two minus X one. Then we get the go to for money to be divided by five minus one and then we get incurred due to over fund what you have. And then because I'm the bourbon Dickler isn't implies down this long We're looking for here Am times in the half year must because u minus one and they found and must Nico Ju minus two and a second information he here will be the by sector by symptom is under point. Here will be go in such a meat point under seven month and a midpoint by former Echo, too. Ah, well, I'm less five. What? You and job less for over two. We're getting good. You 33 So just into information is here, we can have the question becomes, uh why ministry They go to 12 times X minus three. And this will be the key question online We're looking for

Given the um points A and D. We want to find the line that is the perpendicular by sector. So first let's do the perpendicular part. Let's find the slope of a. D. So slope is the difference of your wife fortunes over the difference of your exporting it. So we could say why too is negative two -Y. one which is to over X two which is negative three minus X one which is zero. That's negative four over negative three or four thirds. The perpendicular slope is the opposite reciprocal. So that would be negative 3/4. Now we need the by sector part, that's the main point. The midpoint of a line A segment is The average of the coordinates. So x one plus x. two over to and then why one plus why? 2/2? Which is negative three halves zero. So at negative 1.50 is the midpoint. Which makes sense looking at the graph. And so now we want the equation of a line with the perpendicular slope and it's gonna go um Through the Point -3/2. So using line equals mx plus B, We'll substitute zero for Y -3/4 for X. Excuse me, -3/4 for the slow, -3/2 for X and solve for B. Multiply. And I go through force and I go through has to get 98 and subtract, we get negative 98 is the Y intercept. So our equation is Y equals The perpendicular slope negative three forests minus 98

If we know that point A. Is 0 to 10 point B. Is that four negative one. And we want to find the equation of a perpendicular by sector. So let's first find the slope of baby. That's the difference of your Y coordinates over the difference of your X coordinates. That's a slope of negative three fourths. Now the perpendicular slope Would be the opposite. Reciprocal of your positive for three to be a bio sector needs to go to the mid coin. So the mid coin is X one plus X. Two over to the average of the X coordinates and the average of the Y coordinates. So that would be 4/2 or two and one half. So we want to have an equation of a line using the perpendicular slope and the midpoint. So why is 1/2 M is for thirds X. Is two. And solve for B. We have one half equals eight thirds plus B. Subtract eight thirds. We can get a common denominator of six. So we can say this is 36 in 16 six, So that when we subtract will get negative, 13 6 equals be. So our equation is why equals perpendicular slope X -B, which is 13 6. Yeah.

Eight and with a line segment is given. Who's endpoints are one comma one and three com one. And we need to find a question of perpendicular bisected off this land segment a be This will be OK Now let's Since this is a mere points or letters, you know what? This has em. So midpoint must be three plus one over to one place, one over toe just adding X coordinate and dividing by two and taking why Cornett and development by two for over two comma toe that is two comma one. So we have midpoint to common. One notice. All right. It is excellent. Comma away one forever for the difference. Okay, Now slope of of a given land slope off a be equal to daisy formula for slow That is why to minus one. It means if we're, um yeah, finding the slope off lane segment A B next to it will be the corner of this excellent and will be in the corner of this. So important, though formula slow will be one minus one over three minus one. That is 0/2, which is a little so it's slope is little Good idea and maybe no if you in it the slope off. But Fendick Willa by secretaries and to the product of these two Slow must be minus one. I m in tow. Slope off. Maybe equal to minus one. It means slow. Must be minus one over. Lope off A B. That is slow pickle toe minus one. Over zero letters register here. That it like this? No, If we have slow, we have point. So Christian must be violent. So I'm unequal to m Excellent sex one So we can write is why minus what I want is this excellent This one? Why won't anyone? Excellent is too one snow peas and minus 1/0 X minus two. No, Across my deplane we get zero equal to minus X plus to put in place X equal to two. Which other question off? Perpendicular by sector. Thank you


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