Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
Maintaining Mathematical Proficiency
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Exercise 1 Page 229

Recall the Midpoint and the Distance Formulas.

Midpoint: M(-2,4)
Distance: about 7.2 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 (-4,1) and (0,7). Let's use these to find the coordinates of the midpoint.
M(x_1+x_2/2,y_1+y_2/2)
M(-4+ 0/2,1+ 7/2)
M(-4/2,8/2)
M(-2,4)
The midpoint is located at (-2,4).

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, P(-4,1) and Q(0,7), into this formula and simplify.
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
d=sqrt(( 0-( -4))^2+( 7- 1)^2)
d=sqrt(4^2+(7-1)^2)
d=sqrt(4^2+6^2)
d=sqrt(16+36)
d=sqrt(52)
d≈7.2
The distance between P and Q is sqrt(52), which is approximately 7.2 units.