MATH SOLVE

5 months ago

Q:
# GeometryGiven Triangle DEF with D(-4, -1), E(-1, 8), and F(5,4), find the median DT in point-slope form

Accepted Solution

A:

Answer:

y-6 = (7/6)(x-2)

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Explanation:

The median DT goes from point D, which is given, to point T which we have to find. The point T is the midpoint of segment EF.

Use the midpoint formula to find the midpoint. Add up the x coordinates of E and F to get

-1+5 = 4

Then divide that by 2

4/2 = 2

The x coordinate of point T is x = 2

Repeat for the y coordinates

8+4 = 12

12/2 = 6

The y coordinate of point T is y = 6

So the point T is (x,y) = (2,6)

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We know point D is (-4,-1)

We just found point T to be (2,6)

Using the slope formula, the slope is..

m = (y2-y1)/(x2-x1)

m = (6-(-1))/(2-(-4))

m = (6+1)/(2+4)

m = 7/6

The slope is m = 7/6

Use either the coordinates of D or T. I'll use point T. So (x1,y1) = (2,6) meaning x1 = 2 and y1 = 6

We'll plug m = 7/6, x1 = 2 and y1 = 6 into the point slope equation

y-y1 = m(x-x1)

y-6 = (7/6)(x-2)

which is the final answer

y-6 = (7/6)(x-2)

---------------------------------------------------

Explanation:

The median DT goes from point D, which is given, to point T which we have to find. The point T is the midpoint of segment EF.

Use the midpoint formula to find the midpoint. Add up the x coordinates of E and F to get

-1+5 = 4

Then divide that by 2

4/2 = 2

The x coordinate of point T is x = 2

Repeat for the y coordinates

8+4 = 12

12/2 = 6

The y coordinate of point T is y = 6

So the point T is (x,y) = (2,6)

---------

We know point D is (-4,-1)

We just found point T to be (2,6)

Using the slope formula, the slope is..

m = (y2-y1)/(x2-x1)

m = (6-(-1))/(2-(-4))

m = (6+1)/(2+4)

m = 7/6

The slope is m = 7/6

Use either the coordinates of D or T. I'll use point T. So (x1,y1) = (2,6) meaning x1 = 2 and y1 = 6

We'll plug m = 7/6, x1 = 2 and y1 = 6 into the point slope equation

y-y1 = m(x-x1)

y-6 = (7/6)(x-2)

which is the final answer