Question

1.10.4 Test: Coordinate Geometry HELP PLEASE

Answer 1

Answer:

1.

$M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$M = (-1,4)$

2.

$D = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2}$

$D =10\ units$

Step-by-step explanation:

Solving (1):

1a) This has already been answered in the attachment, and the selected option is correct.

i.e. Midpoint (M) is:

$M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

1b) Midpoint of (-2,-1) and (0,9)

This implies that:

$(x_1,y_1) = (-2,-1)$

$(x_2,y_2) = (0,9)$

So:

$M = (\frac{-2+0}{2},\frac{-1+9}{2})$

$M = (\frac{-2}{2},\frac{8}{2})$

$M = (-1,4)$

2a) This has already been answered in the attachment, and the selected option is correct.

i.e. Distance (D) is:

$D = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2}$

1b) Midpoint of (2,7) and (8,-1)

This implies that:

$(x_1,y_1) = (2,7)$

$(x_2,y_2) = (8,-1)$

So:

$D = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2}$

$D = \sqrt{(8 - 2)^2 +(-1 - 7)^2}$

$D = \sqrt{(6)^2 +(-8)^2}$

$D = \sqrt{36+64}$

$D = \sqrt{100}$

$D =10\ units$