Finding Missing Endpoints Review Finding the midpoint given

Finding Missing Endpoints

Review: Finding the midpoint given two endpoints Find the coordinates of the midpoint of a segment with endpoints R(-12, 8) and S(6, 12)

Now we are GIVEN the midpoint and ONE endpoint. We are looking for the MISSING ENDPOINT! Find the coordinates of the missing endpoint if P is the midpoint of NQ. P is at (6, 3) and N is at (5, 4). N(5, 4) P(6, 3) Normally, when we plug in the x values of our two endpoints, this piece of the midpoint formula gives us the x coordinate of the midpoint. Q(? , ? ) And this piece normally gives us the y coordinate of the midpoint when we plug in the y values of our two endpoints. But, if we plug in our two points, P and N, into the formula like normal, we will be finding the midpoint between P and N, not the missing endpoint!

Find the coordinates of the missing endpoint if P is the midpoint of NQ. P is at (6, 3) and N is at (5, 4). N(5, 4) Since this piece normally GIVES us the x coordinate of the midpoint, we should set it EQUAL to the x-coordinate of the midpoint (P) that we already have! Plug in the xcoordinate of the one endpoint (N) we have into x 2. P(6, 3) Q(? , ? ) Do the same for y. Set this piece of the midpoint formula EQUAL to the y-coordinate of the midpoint (P), and plug in the y value of the one endpoint (N) we have into y 2.

(2) • (2) 5 + x 1 = 12 -5 -5 x 1 = 7 (2) 4 + y 1 = 6 -4 -4 y 1 = 2 The missing endpoint, Q, has coordinates (7, 2)

Find the coordinates of the missing endpoint if P is the midpoint of NQ. P is at (2, 12) and N is at (-8, 1). • (2) (2) -8 + x 1 = 4 1 + y 1 = 24 x 1 = 12 y 1 = 23 +8 +8 -1 -1 The missing endpoint, Q, has coordinates (12, 23)

Find the coordinates of the missing endpoint if P is the midpoint of NQ. P is at (-4, 7) and Q is at (2, -2). • (2) (2) 2 + x 1 = -8 -2 + y 1 = 14 x 1 = -10 y 1 = 16 -2 -2 +2 +2 The missing endpoint, N, has coordinates (-10, 16)

Find the coordinates of the missing endpoint if P is the midpoint of NQ. P is at (-3, 4) and Q is at (5, -2). The missing endpoint, N, has coordinates (-11, 10)

Fractional Distance

To find a fractional distance, multiply the distance times the fractional distance. Ex: Jenny is taking her dog on a 5 mile walk. She wants to stop to take a break after they have completed 2/3 of their walk. Where will she take her break? 5(2/3) = 3. 3 miles

To find the coordinates of a point a fractional distance from one point to another: 2. Multiply this distance by the fractional distance. 3. Add the resulting number to the x value of the point you are going from. This is the x value of the point a fractional distance from the first point. 4. Repeat for the y values.

Find the coordinates of point R that is 1/8 of the way from point S (2, -4) to point T (10, 12) Distance between the y values: Distance between the x values: Multiply the distance by the fractional distance: Add to the x value of S: 2 + 1 = 3 Multiply the distance by the fractional distance: Add to the y value of S: -4 + 2 = -2 The coordinates of R are (3, -2)

Find the coordinates of point R that is ¾ of the way from point S (-8, -6) to point T (-10, -20) -8 + 1. 5 = -6. 5 -6 + 10. 5 = 4. 5 The coordinates of R are (-6. 5, 4. 5)

Find the coordinates of point R that is ¾ of the way from point S (-7, 1) to point T (4, 5) The coordinates of R are (1. 25, 4)