Question

Select the coordinates that are on the line perpendicular to

y=-x-5 and goes through (-3,5)

There are two

a
(-2,6)

b
(4,12)

c
(-3,8)

d
(8,10)

Answer 1

To find the coordinates that are on the line perpendicular to \( y = -x - 5 \) and passes through the point (-3, 5), we first need to determine the slope of the given line.

The equation \( y = -x - 5 \) can be rewritten in slope-intercept form \( y = mx + b \), where \( m \) is the slope. Here, the slope (m) is -1.

Since perpendicular lines have slopes that are negative reciprocals, the slope of the line perpendicular to \( y = -x - 5 \) will be the negative reciprocal of -1, which is 1.

Now, using the point-slope form of the equation of a line, we can write the equation of the line that passes through the point (-3, 5) with a slope of 1:

\[
y - y_1 = m(x - x_1)
\]
\[
y - 5 = 1(x + 3)
\]
\[
y - 5 = x + 3
\]
\[
y = x + 8
\]

Now we need to check which of the given points lie on the line \( y = x + 8 \):

1. For point **a** (-2, 6):
\[
y = -2 + 8 = 6 \quad \text{(this point is on the line)}
\]

2. For point **b** (4, 12):
\[
y = 4 + 8 = 12 \quad \text{(this point is on the line)}
\]

3. For point **c** (-3, 8):
\[
y = -3 + 8 = 5 \quad \text{(this point is not on the line)}
\]

4. For point **d** (8, 10):
\[
y = 8 + 8 = 16 \quad \text{(this point is not on the line)}
\]

Thus, the two points that are on the line perpendicular to \( y = -x - 5 \) and pass through (-3, 5) are:

a. (-2, 6)
b. (4, 12)

So the correct selections are **a** and **b**.