Given that line CD is a perpendicular bisector of triangle ABC, if side AB has a length of 11 and side AC has a length of 14 wha
t is the length of side CD? Write your answer to the
nearest hundredth
nearest hundredth
1 answer:
Answer:
12.87
Step-by-step explanation:
Since we know that line CD is a perpendicular bisector, triangle ACD is a right triangle, and thus we can apply the Pythagorean theorem to determine the length of side CD. Since the Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the adjacent sides, we can plug in the values of side AD and AC.
As side CD is the bisector of side AB, sides AD and DB are both half the length of side AB, so:
AD = 11/2
AD = 5.5
We now know two values of our equation, and thus we can solve for the missing third value.
5.5^2 + b^2 = 14^2
14^2 - 5.5^2 = b^2
196 - 30.25 = b^2
165.75 = b^2
b = 12.87
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Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula . Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):
So, the slope of the line is .
2) Next, use the point-slope formula to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the
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and
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Since represents the slope, substitute
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represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form: