Let A be #(−3,5)# and B be #(5,−10))#. Find: (1) the length of segment #bar(AB)# (2) the midpoint #P# of #bar(AB)# (3) the point #Q# which splits #bar(AB)# in the ratio #2:5#?
(1) the length of the segment
(2) Midpoint of
(3) The coordinates of the point
By signing up, you agree to our Terms of Service and Privacy Policy
- The length of segment ( \overline{AB} ) can be found using the distance formula:
[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]
Given ( A(-3, 5) ) and ( B(5, -10) ), the length of ( \overline{AB} ) is:
[ d = \sqrt{(5 - (-3))^2 + ((-10) - 5)^2} ] [ d = \sqrt{8^2 + (-15)^2} ] [ d = \sqrt{64 + 225} ] [ d = \sqrt{289} ] [ d = 17 ]
So, the length of segment ( \overline{AB} ) is ( 17 ).
- The midpoint ( P ) of segment ( \overline{AB} ) can be found by averaging the coordinates of ( A ) and ( B ):
[ P\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) ]
For ( A(-3, 5) ) and ( B(5, -10) ), the midpoint ( P ) is:
[ P\left(\frac{-3 + 5}{2}, \frac{5 + (-10)}{2}\right) ] [ P\left(\frac{2}{2}, \frac{-5}{2}\right) ] [ P(1, -\frac{5}{2}) ]
So, the midpoint ( P ) of segment ( \overline{AB} ) is ( (1, -\frac{5}{2}) ).
- To find the point ( Q ) which splits ( \overline{AB} ) in the ratio ( 2:5 ), we use the section formula:
[ Q\left(\frac{2x_2 + 5x_1}{2 + 5}, \frac{2y_2 + 5y_1}{2 + 5}\right) ]
For ( A(-3, 5) ) and ( B(5, -10) ), ( Q ) is:
[ Q\left(\frac{2(5) + 5(-3)}{2 + 5}, \frac{2(-10) + 5(5)}{2 + 5}\right) ] [ Q\left(\frac{10 - 15}{7}, \frac{-20 + 25}{7}\right) ] [ Q\left(\frac{-5}{7}, \frac{5}{7}\right) ]
So, the point ( Q ) which splits ( \overline{AB} ) in the ratio ( 2:5 ) is ( \left(\frac{-5}{7}, \frac{5}{7}\right) ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- What is the centroid of a triangle with corners at #(3 , 1 )#, #(2 , 3 )#, and #(5 , 2 )#?
- Find the locus of a point equidistant from two lines #y=sqrt3x# and #y=1/sqrt3x#?
- What is the equation of the perpendicular bisector of the line segment through the points (-2, 6) and (2, -4)?
- What is the difference between medians, perpendicular bisectors, and altitudes?
- A line segment is bisected by a line with the equation # -7 y + 3 x = 2 #. If one end of the line segment is at #( 2 , 1 )#, where is the other end?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7