Question

On a line segment, point A is the midpoint of DC. Given that DA = 40, and AC = 2x + 10, find DC.

A. DC = 2x + 10
B. DC = 80
C. DC = x + 50
D. DC = 2x + 20

Answer 1

To find the length of DC, we need to use the midpoint formula. Given that DA = 40 and AC = 2x + 10, we can substitute the values into the formula and solve for DC. The correct answer is DC = 80.

Step-by-step explanation:

To find the length of DC, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) are given by:

M = ((x1 + x2)/2, (y1 + y2)/2)

In this case, point A is the midpoint of DC, so we can say that A = ((D + C)/2).

Given that DA = 40, we can substitute the value of A into the equation:

40 = ((D + C)/2)

Multiplying both sides by 2:

80 = D + C

Now, we also know that AC = 2x + 10. Substituting the value of C in 80 = D + C with AC gives us:

80 = D + (2x + 10)

Simplifying the equation:

80 = D + 2x + 10

Subtracting 10 from both sides:

D + 2x = 70

So, DC = D + C = 80. Therefore, the correct answer is option B: DC = 80.

Answer 2

To find DC, we need to first find the value of AC. Given that A is the midpoint of DC and DA = 40, we can use the equation DA = AC to solve for x and find the length of AC. By substituting the value of x into the equation AC = 2x + 10, we find that AC = 40. Since A is the midpoint of DC, we know that DC is also equal to 40.

Step-by-step explanation:

To find DC, we need to first find the value of AC. We know that A is the midpoint of DC, so the length of DA is equal to the length of AC. Given that DA = 40, we can substitute this value into the equation: DA = AC. This gives us 40 = 2x + 10. To find the value of x, we solve for x by subtracting 10 from both sides and then dividing both sides by 2. Hence, x = 15. Now that we have the value of x, we can substitute it back into the equation for AC: AC = 2x + 10. This gives us AC = 2(15) + 10 = 30 + 10 = 40. Since A is the midpoint of DC, and AC = DC, we know that DC is also equal to 40. Therefore, the answer is DC = 40, which corresponds to option B.