Big Ideas Math Geometry, 2014
BI
Big Ideas Math Geometry, 2014 View details
2. Bisectors of Triangles
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Exercise 54 Page 318

Recall the Midpoint and the Distance Formulas.

Midpoint: M(-1/2,-2)
AB≈ 10.8 units

Practice makes perfect

Let's find the coordinates of the midpoint and the distance one at a time.

Finding the Midpoint

To find the midpoint M, we can use the Midpoint Formula. M(x_1+x_2/2,y_1+y_2/2)The coordinates of the given endpoints are (-5,1) and (4,-5). Let's use these to find the coordinates of the midpoint.
M(x_1+x_2/2,y_1+y_2/2)
M(-5+ 4/2,1+( -5)/2)
M(-1/2,-4/2)
M(-1/2,-2)
The midpoint is located at (-1/2,-2).

Finding the Distance

To find the distance between the points, we can use the Distance Formula. d=sqrt((x_2-x_1)^2+(y_2-y_1)^2) Let's substitute the given endpoints, A( -5,1) and B( 4,-5), into this formula and simplify.
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
d=sqrt(( 4-( -5))^2+( -5- 1)^2)
d=sqrt((4+5)^2+(-5-1)^2)
d=sqrt(9^2+(-6)^2)
d=sqrt(81+36)
d=sqrt(117)
d≈ 10.8
The distance between A and B is sqrt(117), which is approximately 10.8 units.