All categories

3 years ago

Find an equation for the perpendicular bisector of the line segment whose endpoints are (−3,4) and (−7,−6).

Mathematics

2 answers:

Arte-miy333 [17]3 years ago

7 0

Answer:

She's right, praise jeebus :3

Step-by-step explanation:

sesenic [268]3 years ago

5 0

Answer:

$y=-\frac{2}{5}x-3$

Step-by-step explanation:

First, you must find the midpoint of the segment, the formula for which is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . This gives you (-5,-1) as the midpoint. This is the point at which the segment will be bisected.

Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula $\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$ , which gives us a slope of $\frac{5}{2}$ .

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of $\frac{5}{2}$ is $-\frac{2}{5}$ .

We now know that the perpendicular travels through the point (-5,-1) and has a slope of $-\frac{2}{5}$ .

Solve for $b$ in $y=mx+b$ .

$y=mx+b\\-1=-\frac{2}{5}(-5)+b\\-1=2+b\\-3=b\\b=-3$

Therefore, the equation of the perpendicular bisector is $y=-\frac{2}{5}x-3$ .

You might be interested in

How would I use factoring to write equivalent expressions for the following expressions?

Sedbober [7]

Answer:

4(a + 6)

3(x - 4)

Step-by-step explanation:

Factoring is just rewriting an expression into the parts that multiply together to make the original...like if I had a 100 but decided instead to write 4×25 or if I had 25x I wrote 5(5x) .

If you look at your

4a + 24

You're looking for whatever is the same in both pieces (the 4a and also the 24) So there is a 4 in 4a and there is also a 4 "in" 24 (as in 4×6 is 24)

So if you pull out that 4 and throw it up front, whatever is left behind goes into a pair of parentheses.

4 (____ + ____)

4(a + 6)

This is your factored form bc if you multiply that 4 back in you'll get the original expression back again.

4a + 24

= 4(a + 6)

It's like factoring is "un-distributive" property.

Theres a 3 in 3x and also in 12

3x - 12

= 3(x - 4)

6 0

2 years ago

Manuel climbs a tower from ground level to an elevation of 135 1/2 ft he climbs down 27 1/2 ft how far is Manuel from the ground

Helen [10]

Answer: 108 feet

Step-by-step explanation: (135.5-27.5) = 108 feet

4 0

2 years ago

Read 2 more answers

Using the laws of indices simplify 625^3/8 ×5^1/2÷ 25

Oxana [17]

Answer:

Step-by-step explanation:

$\huge {625}^{ \frac{3}{8} } \times {5}^{ \frac{1}{2} } \div 25 \\ \\ = \huge {( {5}^{4})}^{ \frac{3}{8} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ = \huge{5}^{ \cancel4 \times \frac{3}{ \cancel8 \: \: \red{ \bold 2}} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ \frac{3}{2} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ \frac{3}{2} + \frac{1}{2}} \div {5}^{2} \\ \\ \huge= {5}^{ \frac{4}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ 2 } \div {5}^{2} \\ \\ \huge= {5}^{ 2 - 2 } \\ \\ \huge= {5}^{ 0 } \\ \\ \huge= 1$