Geometry: Triangle QRS is similar to triangle TUV. Write the equation, in slope-intercept form, of the side of triangle QRS that is parallel to segment UV. You must show all work to receive credit. (

Question

I can't put in a diagram because idk why. SRQ is a triangle and VUT is a triangle. The points are as follow, S(-8,1), R(-2,7), Q(-2,1). Now for VUT V(1,2), U(4,5), T(4,2)

Answer 1

I recommend plotting these points on graphing paper to visually see which line of Triangle QRS is parallel to segment UV. If you don't have this option, you can proceed below.

The slope (m) of UV is the change in Y over the change in X for the points U (4,5) and V (1,2)

m = △Y / △X

m =(2 - 5) / (1-4)

m = -3 / -3

m = 1

Now you need to find which points in QRS create a line with a slope of 1 using this same approach. Trying points Q (-2,1) and R (-2,7) first:

m = △Y / △X

m = (7 - 1) / (-2 - -2)

m = 6 / 0

Infinite slope (this is a straight line upwards). This is not parallel.

Let's try R(-2,7) and S (-8, 1) now:

m = △Y / △X

m = (1 - 7) / (-8 - -2)

m = -6 / -6

m = 1

We have a match of slopes for line RS, signifying they are parallel. (Note: If you drew the triangles on graphing paper, you would be able to see line QR was parallel to UV from the start. Then you could determine the equation for the line QR directly solving for the slope, m, (above) and the y-intercept, b, (below)).

Now we need the Y-intercept (b) of this line. We can plug in either one of the two points (R or S) into the slope-intercept form, y = mx + b, and solve for b. Let's use point R.

y = mx + b

(we know the slope, m, is 1; we also can use y is 7 and x is -2 from point R)

7 = 1(-2) + b

(simplify)

7 = -2 + b

(add 2 to both sides)

9 = b

Now with the slope (m) of 1 and y-intercept (b) of 9, we know the equation for line RS is:

y = x + 9