Question

Point B(10,10) is the midpoint of segment AC. Point C is the midpoint of segment AD. If the coordinate of point A is (1,2), then the coordinate of C is _____ and the coordinate of D is _____ .

Answer 1

To find the coordinates of points C and D, the midpoint formula is applied twice. Point C is (19, 18) and point D is (37, 34), satisfying their respective definitions as midpoints of segments AC and AD, with A given as (1,2) and B given as (10,10).

Step-by-step explanation:

If point B(10,10) is the midpoint of segment AC and point A has the coordinates (1,2), we can find the coordinates of point C by using the midpoint formula, which states that the midpoint's coordinates are the averages of the corresponding coordinates of the endpoints. Since B is the midpoint, we have:

• (x-coordinate of A + x-coordinate of C)/2 = x-coordinate of B
• (y-coordinate of A + y-coordinate of C)/2 = y-coordinate of B

Plugging in the values for A and B:

• (1 + x-coordinate of C)/2 = 10
• (2 + y-coordinate of C)/2 = 10

Solving these equations gives us:

• x-coordinate of C = 19
• y-coordinate of C = 18

So, point C is (19, 18).

Since point C is also the midpoint of segment AD, we can use the same formula to find point D. The coordinates of D would satisfy:

• (x-coordinate of A + x-coordinate of D)/2 = x-coordinate of C
• (y-coordinate of A + y-coordinate of D)/2 = y-coordinate of C

Plugging in the known values:

• (1 + x-coordinate of D)/2 = 19
• (2 + y-coordinate of D)/2 = 18

Solving these equations gives us:

• x-coordinate of D = 37
• y-coordinate of D = 34

Therefore, the coordinates of point D are (37, 34).