Question

Use the image to answer the question.

Triangle upper A upper B upper C is plotted on a coordinate plane, which goes from negative 5 to 10 on the x and y axes in intervals of 1 labeled every 5 units.
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The horizontal axis is labeled x and goes from negative 5 to 10 in intervals of 1 labeled every 5 units. The vertical axis is labeled y and goes from negative 5 to 5 in intervals of 1 labeled every 5 units. Vertex upper A is at left parenthesis 2 comma 1 right parenthesis, Vertex upper C is at left parenthesis 6 comma 4 right parenthesis, and vertex upper B is at left parenthesis negative 3 comma negative 5 right parenthesis. There is a line from Vertex upper B to point upper D. Point upper D is on line AC.

If D is the midpoint of AC¯¯¯¯¯¯¯¯
, what is length BD
? Round your answer to the tenths place.

(1 point)
Length BD
is about
units.
Remaining Attempts : 3

Answer 1

A = (2, 1), C = (6, 4). Midpoint D = ((2+6)/2, (1+4)/2) = (4, 2.5).

BD = sqrt[(4 - (-3))^2 + (2.5 - (-5))^2] = sqrt[7^2 + 7.5^2] = sqrt[49 + 56.25] = sqrt[105.25] ≈ 10.3.

Length BD is about 10.3 units.