# Algebra

Find the coordinates of the midpoint of the hypotenuse of the right triangle whose vertices are A (1,1) B (5,2) C (4,6) and show that it is equidistant of each of the vertices.....
And can you please tell me how to prove it in drawing....

1. 👍 0
2. 👎 0
3. 👁 348
1. Your diagram should show that you have a right angle at B , but let's prove it anyway.

slope AB = (2-1)/(5-1) = 1/4
slope of BC = (6-2)/(4-5) = -4
YES, AB is perpendicular to BC, thus AC is a hypotenuse

midpoint of AC = M( (1+4)/2 , (1+6)/2) = M(5/2 , 7/2)
= M(2.5 , 3/5)
AM = √(1.5^2 + 2.5^2 = √8.5
CM = √(1.5^2 + 2.5^2) = √8.5 , clearly has to be, since we found the midpoint
BM = √((5 - 2.5)^2 + (2-3.5)^2 ) = √8.5

YUP, all is good

If you make a good sketch, you should be able to show it by counting the displacements along the grid pattern

1. 👍 0
2. 👎 0
posted by Reiny
2. What is the solution when the formula used is distance between points??

1. 👍 0
2. 👎 0
3. I don't understand your question.
I DID use the distance between two points formula, I just did not show the subtraction since that is easily done in your head.

here is one of them with all steps :
AM = √( 2.5 - 1)^2 + (3.5-1)^2 )
= √( 1.5^2 + 2.5^2)
= √2.25 + 6.25)
= √8.5 ---- see above

= appr 2.9155

1. 👍 0
2. 👎 0
posted by Reiny
4. I mean is to get the distance of A B C you used distance formula not slope...

1. 👍 0
2. 👎 0
5. I think the main purpose of the question, even though they did not say that, was to show that the midpoint of the hypotenuse is equidistant from the 3 vertices.
All I did with the slope calculation was to show that the triangle is indeed right-angled.
Other than that, finding the slope had nothing to do with the calculations of the distances.

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### Math

Triangle ABC has vertices A (-4,-2), B (-1,3), and C (5,0). Triangle ABC is rotated 180 degrees counterclockwise about the origin to form triangle A'B'C'. a. what are the coordinates of the vertices of triangle A'B'C'? b. How

asked by Chill on August 26, 2019
2. ### Math

Triangle ABC has vertices A(–4,–2), B(–1,3), and C(5,0). Triangle ABC is rotated 180° counterclockwise about the origin to form triangle A′B′C′. What are the coordinates of the vertices of the triangle A′B′C′?

asked by Elder on September 9, 2019
3. ### Geometry

I need help with vertices! The vertices of triangle FGH are F(1,1), G(3,-5),H(6,0). Find the coordinates of the vertices after a refelection over the y-axis. I'm not sure how to do this. Is there a certain formula I need to know?

4. ### math

A triangle has vertices with coordinates (2, 0), (3, -1), and (-2, -5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image.

asked by james on December 19, 2013
5. ### math

A triangle has vertices with coordinates (2, 0), (3, -1), and (-2, -5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image.

asked by james on December 19, 2013
1. ### math

Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down. A)Write the coordinated of the vertices of the image after reflection. B)Write a rule for the translation. Use arrow rotation.

asked by gwen on May 18, 2014
2. ### geometry

in triangle GHJ, k(2,3) is the midpoint of GH, l(4,1) is the midpoint of HJ and m(6,2) is the midpoint of GJ. Find the coordinates of G,H and J. can you please show me how to find this? i don't really understand how it would be

asked by maria on November 2, 2010
3. ### math

The vertices of triangle IJK have coordinates I(−5, −2), J(−5, −4), and K(−4, −4). Which coordinates are the coordinates of the vertices of triangle IꞌJꞌKꞌ when triangle IJK is rotated 180° clockwise around the

asked by Potato ^-^ on June 15, 2016
4. ### hialeah miami lakes

given triangle PQR with vertices P(0,-8), Q(4,-9) and R(-2,-3), find the length of the midsegment connecting the midpoint of PQ to the midpoint of PR.

asked by ivette hanon on May 3, 2011
5. ### geometry

in triangle GHJ, K(2,3) is the midpoint of GH, L(4,1) is the midpoint of HJ, M(6,2) is the midpoint of GJ. Find the coordinates of G, H, and J.

asked by brandi on December 9, 2010

More Similar Questions