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II. Determine the coordinates of the midpoint of PQ, if P (-35, 50) and Q (-53, -20).You must write the formula and illustrate the entire procedure.III. A is the mi...

Question

II. Determine the coordinates of the midpoint of PQ, if P (-35, 50) and Q (-53, -20).You must write the formula and illustrate the entire procedure.III. A is the midpoint of BC.BA = 7x - 8 AC = 2x + 12to. Present the diagramDetermine the value of x (17 points)• Present the procedure• justify each step of the procedure using data given in the exercise, definitions, postulates and / or properties >>Using the value of x, determine BA, AC, and BC (23 points)<< Present the procedure a

II. Determine the coordinates of the midpoint of PQ, if P (-35, 50) and Q (-53, -20).You must write the formula and illustrate the entire procedure.III. A is the midpoint of BC.BA = 7x - 8 AC = 2x + 12to. Present the diagramDetermine the value of x (17 points)• Present the procedure• justify each step of the procedure using data given in the exercise, definitions, postulates and / or properties >>Using the value of x, determine BA, AC, and BC (23 points)<< Present the procedure and justify each step of the procedure using definitions, postulates and / or properties >>



Answers

Segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one involving $x$ and the other involving $y .$ Then solve for $x$ and $y .$
$$
P(5,8), M(8,2)
$$

Okay, so we're given one of our endpoints on our midpoint when we want to find our other points. So let's use our midpoint formula. So we know five commentary that's equal to or exploit points. Plus our remaining X points over two and then 10 which is our white points plus are utter. What Once over to tonight, let's set these two equations. You go to each other and we know that five visit with seven plus or two. It's solve for X by multiplying by 10 or two, which gives us 10 and subtracting by seven. So this is three is you go to X in. Here we have three is equal to 10 and plus why over to its multiple ever to And it's a jock 10 To get a native four is equal to our wife. So we see that our cue points were under endpoints is three common negative four

Okay, so we're given P And when we went to find our other endpoints So this is three comma one and then use our midpoint formula. That's going to be our ex points plus our remaining or unknown X points divided by two. And then our white points plus are unknown white points over two. So we know that three is equal to this equation here. So we could set piece suit you cool to each other and then solve for X. So it's multiply both sides right to So we have six and then we're gonna subject the 1.5 to solve for X so six minus 1.5 that you go to a 4.5, which is x a knowledge students Everything for why we have one is equal to 1.25 plus wine over to its multiply by two on both sides. Subtract by 1.25 So this is equipped 0.75 for white. So our cue points that's going to be 4.5 comma 0.75

Okay, so we're giving a point on her mid points and we want to find our other points. So we have three comma two that's equal to our ex points. Plus are unknown X points over two and then r y points, plus our unknown more importance over to So we have that three is equal to 2.5 x over to are actually that 2.5 plus x over two. Let's multiply both sides but to So we got six and then we're gonna subject 2.5 the six minus 2.5 that's equal to a 3.5. So this year is our ex point, and I'll itself for a corresponding why. So that's two is equal to 1.5. That's why over two multiplying by two on both sides were four. And we're going to subtract the 1.75 So this gives us a 2.254 are, um why? And Alex Vines um Okay, so what do we want to do next? Um, finding limit? Yeah, So this gives us where remaining or are other endpoints that is. We have P. This is Q is 3.5 comma, 2.25

So in the human question we have two points P and Q. The coordinates of P is given us minus of square root of seven comma eight times route of three. And the coordinates of Q. And given us five times square root of seven and minus square root of three. And we are told to find the distance between T and Q. And also the midpoint of the line segment joining the points P and Q. So to find the distance between these points, we can use the distance formula which says that the distance between two points say X one comma, Y one and X two comma Y two can be found using the formula which says square root of X two minus X one squared Plus by 2 -91 squared. So then let's take the point expand awareness, P and X. Two Way to ask you then we can write the formula asked five. Group seven minus minus Group seven squired. This is bless minus group three minus eight. Group three squared and this would be equal to five. Route seven minus of minus is plus, so plus route seven squared plus minus Route three minus eight. Route three is minus nine room three squared. So next we have We can add fire route 707 and we will have six groups 7 squared. Bless minus nine Times. Go three Squared. So this is equal to six. Route 7 67 Squared. As it went to 52 and minus. Nayan Times wrote three squared is equal to 2 43. So 2 52 plus 2 43 is equal to 4 95. So we take the square root of 4 95. It is equal to which is equal to 22 point 2 5 units. So this is the distance between the points B and Q. And now to find the midpoint of the lines of men joining these points, we can use the midpoint formula which says That for a nine segment That joins the points X one Y one and X two Y 2. The mid point of this line segment would be at the coordinates X one plus by one. Sorry, X one plus X two divided by two comma Y one plus Y two divided by two. So we took X one Y one S. P. The next two way to ask you. So we can write the formula asked minus square root of seven plus five. Route seven divided by two. And we can take the Y coordinates us eight through three plus minus Route three divided by two. So now we can write minus route seven plus Fire Road seven is fired seven minus Route seven which is four. Route seven divided by two. An april three plus minus Road three is eight or three minus Route three, which is 7 to 3 divided by two so they can divide The four and x coordinate with the two in the denominator. And we would have to Route seven comma 7 to 3, divided by two As the mid point of the line segment, joining the points PN two. So these are the required answers. I hope you understood the method. Thank you.


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